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Note on: “Sparse domination results for compactness on weighted spaces” 说明："加权空间紧凑性的稀疏支配结果"
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-09-14 DOI: 10.1007/s13348-024-00453-9
Cody B. Stockdale, Paco Villarroya, Brett D. Wick
{"title":"Note on: “Sparse domination results for compactness on weighted spaces”","authors":"Cody B. Stockdale, Paco Villarroya, Brett D. Wick","doi":"10.1007/s13348-024-00453-9","DOIUrl":"https://doi.org/10.1007/s13348-024-00453-9","url":null,"abstract":"<p>An incomplete argument for Theorem 1.4 of Stockdale et al. (Collect Math 73(3):535–563, 2022) is corrected. The validity of Stockdale et al. (Collect Math 73(3):535–563, 2022, Theorem 2.7) remains open.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254379","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}
引用次数: 0
Gorenstein modules and dimension over large families of infinite groups 无穷群大家族上的戈伦斯坦模块和维度
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-09-14 DOI: 10.1007/s13348-024-00454-8
Dimitra-Dionysia Stergiopoulou
{"title":"Gorenstein modules and dimension over large families of infinite groups","authors":"Dimitra-Dionysia Stergiopoulou","doi":"10.1007/s13348-024-00454-8","DOIUrl":"https://doi.org/10.1007/s13348-024-00454-8","url":null,"abstract":"<p>We give characterizations of Gorenstein projective, Gorenstein flat and Gorenstein injective modules over the group algebra for large families of infinite groups and show that every weak Gorenstein projective, weak Gorenstein flat and weak Gorenstein injective module is Gorenstein projective, Gorenstein flat and Gorenstein injective, respectively. These characterizations provide Gorenstein analogues of Benson’s cofibrant modules. We deduce that, over a commutative ring of finite Gorenstein weak global dimension, every Gorenstein projective module is Gorenstein flat. Moreover, we study cases where the tensor product and the group of homomorphisms between modules over the group algebra is a Gorenstein module. Finally, we determine the Gorenstein homological dimension of an <span>({{textbf {LH}}}mathfrak {F})</span>-group over a commutative ring of finite Gorenstein weak global dimension.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254372","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}
引用次数: 0
Free decomposition spaces 自由分解空间
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-09-02 DOI: 10.1007/s13348-024-00446-8
Philip Hackney, Joachim Kock
{"title":"Free decomposition spaces","authors":"Philip Hackney, Joachim Kock","doi":"10.1007/s13348-024-00446-8","DOIUrl":"https://doi.org/10.1007/s13348-024-00446-8","url":null,"abstract":"<p>We introduce the notion of free decomposition spaces: they are simplicial spaces freely generated by inert maps. We show that left Kan extension along the inclusion takes general objects to Möbius decomposition spaces and general maps to CULF maps. We establish an equivalence of <span>(infty )</span>-categories <img alt=\"\" src=\"//media.springernature.com/lw177/springer-static/image/art%3A10.1007%2Fs13348-024-00446-8/MediaObjects/13348_2024_446_IEq3_HTML.gif\" style=\"width:177px;max-width:none;\"/>. Although free decomposition spaces are rather simple objects, they abound in combinatorics: it seems that all comultiplications of deconcatenation type arise from free decomposition spaces. We give an extensive list of examples, including quasi-symmetric functions.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210242","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}
引用次数: 0
On a regularity-conjecture of generalized binomial edge ideals 关于广义二项式边理想的正则猜想
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-08-20 DOI: 10.1007/s13348-024-00452-w
J. Anuvinda, Ranjana Mehta, Kamalesh Saha
{"title":"On a regularity-conjecture of generalized binomial edge ideals","authors":"J. Anuvinda, Ranjana Mehta, Kamalesh Saha","doi":"10.1007/s13348-024-00452-w","DOIUrl":"https://doi.org/10.1007/s13348-024-00452-w","url":null,"abstract":"<p>In this paper, we prove the upper bound conjecture proposed by Saeedi Madani and Kiani on the Castelnuovo–Mumford regularity of generalized binomial edge ideals. We give a combinatorial upper bound of regularity for generalized binomial edge ideals, which is better than the bound claimed in that conjecture. Also, we show that the bound is tight by providing an infinite class of graphs.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226693","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}
引用次数: 0
A study of $${textrm{v}}$$ -number for some monomial ideals 某些单项式理想的 $${textrm{v}}$ 数的研究
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-08-19 DOI: 10.1007/s13348-024-00451-x
Prativa Biswas, Mousumi Mandal
{"title":"A study of $${textrm{v}}$$ -number for some monomial ideals","authors":"Prativa Biswas, Mousumi Mandal","doi":"10.1007/s13348-024-00451-x","DOIUrl":"https://doi.org/10.1007/s13348-024-00451-x","url":null,"abstract":"<p>In this paper, we give formulas for <span>({textrm{v}})</span>-number of edge ideals of some graphs like path, cycle, 1-clique sum of a path and a cycle, 1-clique sum of two cycles and join of two graphs. For an <span>({mathfrak {m}})</span>-primary monomial ideal <span>(Isubset S=K[x_1,ldots ,x_t])</span>, we provide an explicit expression of <span>({textrm{v}})</span>-number of <i>I</i>, denoted by <span>({textrm{v}}(I))</span>, and give an upper bound of <span>({textrm{v}}(I))</span> in terms of the degree of its generators. We show that for a monomial ideal <i>I</i>, <span>({textrm{v}}(I^{n+1}))</span> is bounded above by a linear polynomial for large <i>n</i> and for certain classes of monomial ideals, the upper bound is achieved for all <span>(nge 1)</span>. For <span>({mathfrak {m}})</span>-primary monomial ideal <i>I</i> we prove that <span>({textrm{v}}(I)le {text {reg}}(S/I))</span> and their difference can be arbitrarily large.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210243","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}
引用次数: 0
Local structure of the Teichmüller and the Riemann moduli stacks 泰赫米勒模数堆栈和黎曼模数堆栈的局部结构
IF 0.7 2区 数学
Collectanea Mathematica Pub Date : 2024-08-09 DOI: 10.1007/s13348-024-00450-y
A. Doan
{"title":"Local structure of the Teichmüller and the Riemann moduli stacks","authors":"A. Doan","doi":"10.1007/s13348-024-00450-y","DOIUrl":"https://doi.org/10.1007/s13348-024-00450-y","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141923486","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}
引用次数: 0
Polynomial growth of Betti sequences over local rings 局部环上贝蒂序列的多项式增长
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-08-04 DOI: 10.1007/s13348-024-00449-5
Luchezar L. Avramov, Alexandra Seceleanu, Zheng Yang
{"title":"Polynomial growth of Betti sequences over local rings","authors":"Luchezar L. Avramov, Alexandra Seceleanu, Zheng Yang","doi":"10.1007/s13348-024-00449-5","DOIUrl":"https://doi.org/10.1007/s13348-024-00449-5","url":null,"abstract":"<p>This is a study of the sequences of Betti numbers of finitely generated modules over a complete intersection local ring, <i>R</i>. The subsequences <span>((beta ^R_i(M)))</span> with even, respectively, odd <i>i</i> are known to be eventually given by polynomials in <i>i</i> with equal leading terms. We show that these polynomials coincide if <span>({{I}{}^{scriptscriptstyle square }})</span>, the ideal generated by the quadratic relations of the associated graded ring of <i>R</i>, satisfies <span>({text {height}}{{I}{}^{scriptscriptstyle square }} ge {text {codim}}R -1)</span>, and that the converse holds if <i>R</i> is homogeneous or <span>({text {codim}}R le 4)</span>. Subsequently Avramov, Packauskas, and Walker proved that the terms of degree <span>(j &gt; {text {codim}}R -{text {height}}{{I}{}^{scriptscriptstyle square }})</span> of the even and odd Betti polynomials are equal. We give a new proof of that result, based on an intrinsic characterization of residue rings of c.i. local rings of minimal multiplicity obtained in this paper. We also show that that bound is optimal.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944603","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}
引用次数: 0
Irreducible modules over the Lie conformal algebra $${mathfrak {B}}(alpha ,beta ,p)$$ 列共形代数 $${mathfrak {B}}(alpha ,beta ,p)$$ 上的不可还原模块
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-06-24 DOI: 10.1007/s13348-024-00448-6
Haibo Chen, Yanyong Hong, Yucai Su
{"title":"Irreducible modules over the Lie conformal algebra $${mathfrak {B}}(alpha ,beta ,p)$$","authors":"Haibo Chen, Yanyong Hong, Yucai Su","doi":"10.1007/s13348-024-00448-6","DOIUrl":"https://doi.org/10.1007/s13348-024-00448-6","url":null,"abstract":"<p>In this paper, we introduce a class of infinite Lie conformal algebras <span>({mathfrak {B}}(alpha ,beta ,p))</span>, which are the semi-direct sums of Block type Lie conformal algebra <span>({mathfrak {B}}(p))</span> and its non-trivial conformal modules of <span>({mathbb {Z}})</span>-graded free intermediate series. The annihilation algebras are a class of infinite-dimensional Lie algebras, which include a lot of interesting subalgebras: Virasoro algebra, Block type Lie algebra, twisted Heisenberg–Virasoro algebra and so on. We give a complete classification of all finite non-trivial irreducible conformal modules of <span>({mathfrak {B}}(alpha ,beta ,p))</span> for <span>(alpha ,beta in {mathbb {C}}, pin {mathbb {C}}^*)</span>. As an application, the classifications of finite irreducible conformal modules over a series of finite Lie conformal algebras <span>({mathfrak {b}}(n))</span> for <span>(nge 1)</span> are given.\u0000</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530159","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}
引用次数: 0
Quadric cones on the boundary of the Mori cone for very general blowups of the plane 莫里锥边界上的四角锥，适用于非常一般的平面吹胀
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-06-18 DOI: 10.1007/s13348-024-00447-7
Ciro Ciliberto, Rick Miranda, Joaquim Roé
{"title":"Quadric cones on the boundary of the Mori cone for very general blowups of the plane","authors":"Ciro Ciliberto, Rick Miranda, Joaquim Roé","doi":"10.1007/s13348-024-00447-7","DOIUrl":"https://doi.org/10.1007/s13348-024-00447-7","url":null,"abstract":"<p>In this paper we show the existence of cones over a 8-dimensional rational sphere at the boundary of the Mori cone of the blow-up of the plane at <span>(sge 13)</span> very general points. This gives evidence for De Fernex’s strong <span>(Delta )</span>-conjecture, which is known to imply Nagata’s conjecture. This also implies the existence of a multitude of good and wonderful rays as defined in Ciliberto et al. (Clay Math Proc 18:185–203, 2013).</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510988","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}
引用次数: 0
Convex hulls of surfaces in fourspace 四空间曲面的凸壳
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-05-29 DOI: 10.1007/s13348-024-00444-w
Chiara Meroni, Kristian Ranestad, Rainer Sinn
{"title":"Convex hulls of surfaces in fourspace","authors":"Chiara Meroni, Kristian Ranestad, Rainer Sinn","doi":"10.1007/s13348-024-00444-w","DOIUrl":"https://doi.org/10.1007/s13348-024-00444-w","url":null,"abstract":"<p>This is a case study of the algebraic boundary of convex hulls of varieties. We focus on surfaces in fourspace to showcase new geometric phenomena that neither curves nor hypersurfaces exhibit. Our method is a detailed analysis of a general purpose formula by Ranestad and Sturmfels in the case of smooth real algebraic surfaces of low degree (that are rational over the complex numbers). We study both the complex and the real features of the algebraic boundary of Veronese and Del Pezzo surfaces. The main difficulties and the possible approaches to the case of general surfaces are discussed for and complemented by the example of Bordiga surfaces.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141188551","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}
引用次数: 0
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