Journal of Pure and Applied Algebra最新文献

{"title":"Weight conjectures for Parker–Semeraro fusion systems","authors":"Radha Kessar ,&nbsp;Jason Semeraro ,&nbsp;Patrick Serwene ,&nbsp;İpek Tuvay","doi":"10.1016/j.jpaa.2025.108140","DOIUrl":"10.1016/j.jpaa.2025.108140","url":null,"abstract":"<div><div>We prove that the Parker–Semeraro systems satisfy six of the nine Kessar–Linckelmann–Lynd–Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the principal 3-block of <span><math><mrow><mi>Aut</mi></mrow><mo>(</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mn>3</mn><mo>)</mo><mo>)</mo></math></span>, the principal 5-blocks of <em>HN</em>, <em>BM</em>, <span><math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>H</mi><mi>N</mi><mo>)</mo></math></span>, <em>Ly</em>, the principal 7-block of <em>M</em>, and the principal <em>p</em>-blocks of <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>p</mi><mo>)</mo></math></span> for <span><math><mi>p</mi><mo>≥</mo><mn>3</mn></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108140"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear subspaces of the intersection of two quadrics via Kuznetsov component","authors":"Yanjie Li ,&nbsp;Shizhuo Zhang","doi":"10.1016/j.jpaa.2025.108096","DOIUrl":"10.1016/j.jpaa.2025.108096","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> be 2<em>g</em> dimensional quadrics in <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn><mi>g</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> and let <em>Y</em> be the smooth intersection <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∩</mo><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. We associate the linear subspaces in <em>Y</em> with vector bundles on the hyperelliptic curve <em>C</em> of genus <em>g</em> via categorical methods. As an application, we give a different proof of the classification of line bundles and stable bundles of rank 2 on hyperelliptic curves given by Desale and Ramanan. When <span><math><mi>g</mi><mo>=</mo><mn>3</mn></math></span>, we show that the projection functor induces a closed embedding <span><math><mi>α</mi><mo>:</mo><mi>Y</mi><mo>→</mo><mi>S</mi><msubsup><mrow><mi>U</mi></mrow><mrow><mi>C</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>(</mo><mn>4</mn><mo>,</mo><mi>h</mi><mo>)</mo></math></span> into the moduli space of stable bundles on <em>C</em> of rank 4 of fixed determinant.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108096"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the average degree of characters with odd or even degrees","authors":"Kamal Aziziheris ,&nbsp;Necat Gorentas ,&nbsp;Zinah Naser Sulaiman","doi":"10.1016/j.jpaa.2025.108098","DOIUrl":"10.1016/j.jpaa.2025.108098","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>acd</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the average degree of irreducible characters of <em>G</em> with odd degree. It has been proved that if <span><math><msub><mrow><mi>acd</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>&lt;</mo><msub><mrow><mi>acd</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><msub><mrow><mtext>A</mtext></mrow><mrow><mn>5</mn></mrow></msub><mo>)</mo><mo>=</mo><mn>3</mn></math></span>, then <em>G</em> is a solvable group. On the other hand, let <span><math><msub><mrow><mi>acd</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the average degree of linear characters and irreducible characters of <em>G</em> with even degree. It has been shown that if <span><math><msub><mrow><mi>acd</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>&lt;</mo><msub><mrow><mi>acd</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msub><mrow><mtext>A</mtext></mrow><mrow><mn>5</mn></mrow></msub><mo>)</mo><mo>=</mo><mn>5</mn><mo>/</mo><mn>2</mn></math></span>, then <em>G</em> is a solvable group. In this paper, we improve these bounds and we show that if <em>G</em> is a finite group with <span><math><msub><mrow><mi>acd</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>&lt;</mo><msub><mrow><mi>acd</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><mrow><mi>PSL</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>)</mo><mo>=</mo><mn>7</mn><mo>/</mo><mn>2</mn></math></span>, then either <em>G</em> is a solvable group or <em>G</em> has a chief factor isomorphic to <span><math><msub><mrow><mtext>A</mtext></mrow><mrow><mn>5</mn></mrow></msub></math></span>. Also, we prove that if <em>G</em> is a finite group with <span><math><msub><mrow><mi>acd</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>&lt;</mo><msub><mrow><mi>acd</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mrow><mi>PSL</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>)</mo><mo>=</mo><mn>9</mn><mo>/</mo><mn>2</mn></math></span>, then either <em>G</em> is a solvable group or all minimal normal subgroups of <em>G</em> are abelian or isomorphic to <span><math><msub><mrow><mtext>A</mtext></mrow><mrow><mn>5</mn></mrow></msub></math></span>. Clearly, these bounds are the best.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108098"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On definable subcategories","authors":"Ramin Ebrahimi","doi":"10.1016/j.jpaa.2025.108118","DOIUrl":"10.1016/j.jpaa.2025.108118","url":null,"abstract":"<div><div>Let <span><math><mi>X</mi></math></span> be a skeletally small additive category. Using the canonical equivalence between two different presentations of the free abelian category over <span><math><mi>X</mi></math></span>, we give a new and simple characterization of definable subcategories of <span><math><mi>Mod</mi><mspace></mspace><mtext>-</mtext><mi>X</mi></math></span>, and in particular definable subcategories of modules over rings. In the end, we give a conceptual proof of Auslander-Gruson-Jensen duality, which makes the duality between definable subcategories of left and right module more transparent.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108118"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On isotropy groups of quantum plane","authors":"Adriano De Santana ,&nbsp;Rene Baltazar ,&nbsp;Robson Vinciguerra ,&nbsp;Wilian De Araujo","doi":"10.1016/j.jpaa.2025.108095","DOIUrl":"10.1016/j.jpaa.2025.108095","url":null,"abstract":"<div><div>This paper investigates the isotropy groups of derivations on the Quantum Plane <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>]</mo></math></span>, defined by the relation <span><math><mi>y</mi><mi>x</mi><mo>=</mo><mi>q</mi><mi>x</mi><mi>y</mi></math></span>, where <span><math><mi>q</mi><mo>∈</mo><msup><mrow><mi>k</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, with <span><math><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>≠</mo><mn>1</mn></math></span>. The main goal is to determine the automorphisms of the Quantum Plane that commutes with a fixed derivation <em>δ</em>. We describe conditions under which the isotropy group <span><math><msub><mrow><mtext>Aut</mtext></mrow><mrow><mi>δ</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is trivial, finite, or infinite, depending on the structure of <em>δ</em> and whether <em>q</em> is a root of unity: additionally, we present the structure of the group in the finite case. A key tool is the analysis of polynomial equations of the form <span><math><msubsup><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>a</mi></mrow></msubsup><msubsup><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>b</mi></mrow></msubsup><mo>=</mo><mn>1</mn></math></span>, arising from monomials in the inner part of <em>δ</em>. We also make explicit which finite subgroups of <span><math><mi>Aut</mi><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>]</mo><mo>)</mo></math></span> are isotropy groups of some derivation: either <em>q</em> root of unity or not. Techniques from algebraic geometry, such as intersection multiplicity, are also employed in the classification of the finite case.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108095"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reconstruction of hypersurfaces from their invariants","authors":"Thomas Bouchet","doi":"10.1016/j.jpaa.2025.108109","DOIUrl":"10.1016/j.jpaa.2025.108109","url":null,"abstract":"<div><div>Let <em>K</em> be a field of characteristic 0. We present an explicit algorithm that, given the invariants of a generic homogeneous polynomial <em>f</em> under the linear action of <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> or <span><math><msub><mrow><mi>SL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, returns a polynomial differing from <em>f</em> only by a linear change of variables with coefficients in a finite extension of <em>K</em>. Our approach uses the theory of covariants and the Veronese embeddings to characterize the linear equivalence class of a homogeneous polynomial through equations whose coefficients are invariants. As applications, we derive explicit formulas for reconstructing of a generic non-hyperelliptic curve of genus 4 from its invariants, as well as reconstructing generic non-hyperelliptic curves of genus 3 from their Dixmier-Ohno invariants. Formulas for the reconstruction of cubic surfaces from their Salmon-Clebsch invariants. In all of these cases, the coefficients of the reconstructed object lie in its field of moduli.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108109"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite groups with the minimal generating set exchange property","authors":"Andrea Lucchini ,&nbsp;Patricia Medina Capilla","doi":"10.1016/j.jpaa.2025.108114","DOIUrl":"10.1016/j.jpaa.2025.108114","url":null,"abstract":"<div><div>Let <span><math><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the smallest cardinality of a generating set of a finite group <em>G</em>. We give a complete classification of the finite groups with the property that, whenever <span><math><mo>〈</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><mo>〉</mo><mo>=</mo><mo>〈</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><mo>〉</mo><mo>=</mo><mi>G</mi></math></span>, for any <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> there exists <span><math><mn>1</mn><mo>≤</mo><mi>j</mi><mo>≤</mo><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> such that <span><math><mo>〈</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><mo>〉</mo><mo>=</mo><mi>G</mi></math></span>. We also prove that for every finite group <em>G</em> and every maximal subgroup <em>M</em> of <em>G</em>, there exists a generating set for <em>G</em> of minimal size in which at least <span><math><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>−</mo><mn>2</mn></math></span> elements belong to <em>M</em>. We conjecture that the stronger statement holds, that there exists a generating set of size <span><math><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> in which only one element does not belong to <em>M</em>, and we prove this conjecture for some suitable choices of <em>M</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108114"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2","authors":"Saïd Benayadi ,&nbsp;Sofiane Bouarroudj ,&nbsp;Quentin Ehret","doi":"10.1016/j.jpaa.2025.108086","DOIUrl":"10.1016/j.jpaa.2025.108086","url":null,"abstract":"<div><div>The purpose of this paper is twofold. First, we introduce the notions of left-symmetric and left-alternative structures on superspaces in characteristic 2. We describe their main properties and classify them in dimension 2. We show that left-symmetric structures can be queerified if and only if they are left-alternative.</div><div>Secondly, we present a method of Lagrangian extension of Lie superalgebras in characteristic 2 with a flat torsion-free connection. We show that any strongly polarized quasi-Frobenius Lie superalgebra can be obtained as a Lagrangian extension. Further, we demonstrate that Lagrangian extensions are classified by a certain cohomology space that we introduce. To illustrate our constructions, all Lagrangian extensions in dimension 4 have been described.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108086"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145107307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Picard number and the extension degree of period matrices of complex tori","authors":"Robert Auffarth ,&nbsp;Jorge Duque Franco","doi":"10.1016/j.jpaa.2025.108097","DOIUrl":"10.1016/j.jpaa.2025.108097","url":null,"abstract":"<div><div>The rank <em>ρ</em> of the Néron-Severi group of a complex torus <em>X</em> of dimension <em>g</em> satisfies <span><math><mn>0</mn><mo>≤</mo><mi>ρ</mi><mo>≤</mo><msup><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>. The degree <span><math><mi>d</mi></math></span> of the extension field generated over <span><math><mi>Q</mi></math></span> by the entries of a period matrix of <em>X</em> imposes constraints on its Picard number <em>ρ</em> and, consequently, on the structure of <em>X</em>. In this paper, we show that when <span><math><mi>d</mi></math></span> is 2, 3, or 4, the Picard number <em>ρ</em> is necessarily large. Moreover, for an abelian variety <em>X</em> of dimension <em>g</em> with <span><math><mi>d</mi><mo>=</mo><mn>3</mn></math></span>, we establish a structure-type result: <em>X</em> must be isogenous to <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>g</mi></mrow></msup></math></span>, where <em>E</em> is an elliptic curve without complex multiplication. In this case, the Picard number satisfies <span><math><mi>ρ</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>g</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>. As a byproduct, we obtain that if <span><math><mi>d</mi></math></span> is odd, then <span><math><mi>ρ</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>≤</mo><mfrac><mrow><mi>g</mi><mo>(</mo><mi>g</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108097"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computing epsilon multiplicities in graded algebras","authors":"Suprajo Das ,&nbsp;Saipriya Dubey ,&nbsp;Sudeshna Roy ,&nbsp;Jugal K. Verma","doi":"10.1016/j.jpaa.2025.108107","DOIUrl":"10.1016/j.jpaa.2025.108107","url":null,"abstract":"<div><div>This article investigates the computational aspects of the <em>ε</em>-multiplicity. Primarily, we show that the <em>ε</em>-multiplicity of a homogeneous ideal <em>I</em> in a two-dimensional standard graded domain of finite type over an algebraically closed field of arbitrary characteristic, is always a rational number. In this situation, we produce a formula for the <em>ε</em>-multiplicity of <em>I</em> in terms of certain mixed multiplicities associated to <em>I</em>. In any dimension, under the assumptions that the saturated Rees algebra of <em>I</em> is finitely generated, we give a different expression of the <em>ε</em>-multiplicity in terms of mixed multiplicities by using the Veronese degree. This enabled us to make various explicit computations of <em>ε</em>-multiplicities. We further write a Macaulay2 algorithm to compute <em>ε</em>-multiplicity (under the Noetherian hypotheses) even when the base ring is not necessarily standard graded.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108107"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}