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The Tor Algebra of Trimmings of Gorenstein Ideals 戈伦斯坦理想的修剪的托尔代数
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-12-13 DOI: 10.1007/s40306-023-00512-6
Luigi Ferraro, Alexis Hardesty
{"title":"The Tor Algebra of Trimmings of Gorenstein Ideals","authors":"Luigi Ferraro,&nbsp;Alexis Hardesty","doi":"10.1007/s40306-023-00512-6","DOIUrl":"10.1007/s40306-023-00512-6","url":null,"abstract":"<div><p>Let <span>((R,mathfrak m,Bbbk ))</span> be a regular local ring of dimension 3. Let <i>I</i> be a Gorenstein ideal of <i>R</i> of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that <i>I</i> is generated by the sub-maximal pfaffians of this matrix. Let <i>J</i> be the ideal obtained by multiplying some of the pfaffian generators of <i>I</i> by <span>(mathfrak m)</span>; we say that <i>J</i> is a trimming of <i>I</i>. Building on a recent paper of Vandebogert, we construct an explicit free resolution of <i>R/J</i> and compute a partial DG algebra structure on this resolution. We provide the full DG algebra structure in the appendix. We use the products on this resolution to study the Tor algebra of such trimmed ideals and we use the information obtained to prove that recent conjectures of Christensen, Veliche and Weyman on ideals of class <span>(textbf{G})</span> hold true in our context. Furthermore, we address the realizability question for ideals of class <span>(textbf{G})</span>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Set of Chern Numbers in Local Rings 论局部环中的切尔数集
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-12-05 DOI: 10.1007/s40306-023-00517-1
Le Truong Hoang, Ngoc Yen Hoang
{"title":"On the Set of Chern Numbers in Local Rings","authors":"Le Truong Hoang,&nbsp;Ngoc Yen Hoang","doi":"10.1007/s40306-023-00517-1","DOIUrl":"10.1007/s40306-023-00517-1","url":null,"abstract":"<div><p>The purpose of this paper is to characterize Noetherian local rings <span>((R, mathfrak {m}))</span> such that the Chern numbers of certain <span>(mathfrak {m})</span>-primary ideals in <i>R</i> are bounded above or range among only finitely many values. Consequently, we characterize the Gorensteinness, Cohen-Macaulayness, and generalized Cohen-Macaulayness of local rings in terms of the behavior of their Chern numbers.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138601167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic 论素性环的弗罗贝纽斯代数的无限生成焦点
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-12-05 DOI: 10.1007/s40306-023-00515-3
Alberto F. Boix, Danny A. J. Gómez–Ramírez, Santiago Zarzuela
{"title":"On the Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic","authors":"Alberto F. Boix,&nbsp;Danny A. J. Gómez–Ramírez,&nbsp;Santiago Zarzuela","doi":"10.1007/s40306-023-00515-3","DOIUrl":"10.1007/s40306-023-00515-3","url":null,"abstract":"<div><p>Let <i>R</i> be a commutative Noetherian ring of prime characteristic <i>p</i>. The main goal of this paper is to study in some detail when </p><div><div><span>$$ {mathfrak {p}in {text {Spec}} (R),:, mathcal {F}^{E_{mathfrak {p}}}text { is finitely generated as a ring over its degree zero piece}} $$</span></div></div><p>is an open set in the Zariski topology, where <span>(mathcal {F}^{E_{mathfrak {p}}})</span> denotes the Frobenius algebra attached to the injective hull of the residue field of <span>(R_{mathfrak {p}}.)</span> We show that this is true when <i>R</i> is a Stanley–Reisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Noetherian Rings of the Form ({mathcal {A}}[X,Y;lambda ]) Noetherian Rings of the Form （{mathcal {A}}[X,Y;lambda ])
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-11-11 DOI: 10.1007/s40306-023-00516-2
Abdelamir Dabbabi, Ali Benhissi
{"title":"Noetherian Rings of the Form ({mathcal {A}}[X,Y;lambda ])","authors":"Abdelamir Dabbabi,&nbsp;Ali Benhissi","doi":"10.1007/s40306-023-00516-2","DOIUrl":"10.1007/s40306-023-00516-2","url":null,"abstract":"<div><p>In this paper, we use composite ring extensions to construct a new class of Noetherian rings. Composite ring extensions are examples of pullback constructions, and they are useful in constructing of (counter)-examples.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Numerical Solution to an Inverse Medium Scattering Problem 关于反介质散射问题的数值解法
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-11-06 DOI: 10.1007/s40306-023-00513-5
Dinh-Liem Nguyen, Trung Truong
{"title":"On the Numerical Solution to an Inverse Medium Scattering Problem","authors":"Dinh-Liem Nguyen,&nbsp;Trung Truong","doi":"10.1007/s40306-023-00513-5","DOIUrl":"10.1007/s40306-023-00513-5","url":null,"abstract":"<div><p>This paper is concerned with the inverse medium scattering problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering object in a fast and robust way. A flexibility of this indicator function is that it is applicable to data measured in near-field regime or far-field regime. The implementation of the function is simple and does not involve solving any ill-posed problems. The resolution analysis and stability estimate of the indicator function are investigated using the factorization analysis of the far-field operator along with the Funk-Hecke formula. The performance of the method is verified on both simulated and experimental data.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135636959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Taylor Polynomials of Rational Functions 有理函数的泰勒多项式
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-11-03 DOI: 10.1007/s40306-023-00514-4
Aldo Conca, Simone Naldi, Giorgio Ottaviani, Bernd Sturmfels
{"title":"Taylor Polynomials of Rational Functions","authors":"Aldo Conca,&nbsp;Simone Naldi,&nbsp;Giorgio Ottaviani,&nbsp;Bernd Sturmfels","doi":"10.1007/s40306-023-00514-4","DOIUrl":"10.1007/s40306-023-00514-4","url":null,"abstract":"<div><p>A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, Taylor varieties are given by rank constraints on Hankel matrices. Inversion of the natural parametrization is known as Padé approximation. We study the dimension and defining ideals of Taylor varieties. Taylor hypersurfaces are interesting for projective geometry, since their Hessians tend to vanish. In three and more variables, there exist defective Taylor varieties whose dimension is smaller than the number of parameters. We explain this with Fröberg’s Conjecture in commutative algebra.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Leavitt Path Algebras of Hopf Graphs 论霍普夫图的莱维特路径代数
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-09-19 DOI: 10.1007/s40306-023-00511-7
T. G. Nam, N. T. Phuc
{"title":"On Leavitt Path Algebras of Hopf Graphs","authors":"T. G. Nam,&nbsp;N. T. Phuc","doi":"10.1007/s40306-023-00511-7","DOIUrl":"10.1007/s40306-023-00511-7","url":null,"abstract":"<div><p>In this paper, we provide the structure of Hopf graphs associated to pairs <span>((G, mathfrak {r}))</span> consisting of groups <i>G</i> together with ramification datas <span>(mathfrak {r})</span> and their Leavitt path algebras. Consequently, we characterize the Gelfand-Kirillov dimension, the stable rank, the purely infinite simplicity and the existence of a nonzero finite dimensional representation of the Leavitt path algebra of a Hopf graph via properties of ramification data <span>(mathfrak {r})</span> and <i>G</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135015875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Respondent-Driven Sampling on Sparse Erdös-Rényi Graphs 稀疏Erdös-Rényi图的响应驱动抽样
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2023-09-12 DOI: 10.1007/s40306-023-00510-8
Anthony Cousien, Jean-Stéphane Dhersin, Viet Chi Tran, Thi Phuong Thuy Vo
{"title":"Respondent-Driven Sampling on Sparse Erdös-Rényi Graphs","authors":"Anthony Cousien,&nbsp;Jean-Stéphane Dhersin,&nbsp;Viet Chi Tran,&nbsp;Thi Phuong Thuy Vo","doi":"10.1007/s40306-023-00510-8","DOIUrl":"10.1007/s40306-023-00510-8","url":null,"abstract":"<div><p>We study the exploration of an Erdös-Rényi random graph by a respondent-driven sampling method, where discovered vertices reveal their neighbors. Some of them receive coupons to reveal in their turn their own neighborhood. This leads to the study of a Markov chain on the random graph that we study. For sparse Erdös-Rényi graphs of large sizes, this process correctly renormalized converges to the solution of a deterministic curve, solution of a system of ODEs absorbed on the abscissa axis. The associated fluctuation process is also studied, providing a functional central limit theorem, with a Gaussian limiting process. Simulations and numerical computation illustrate the study.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50476179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cone of Maximal Subextensions of the Plurisubharmonic Functions 多次调和函数的极大子扩展锥
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-08-05 DOI: 10.1007/s40306-023-00509-1
Le Mau Hai, Pham Hoang Hiep, Trinh Tung
{"title":"Cone of Maximal Subextensions of the Plurisubharmonic Functions","authors":"Le Mau Hai,&nbsp;Pham Hoang Hiep,&nbsp;Trinh Tung","doi":"10.1007/s40306-023-00509-1","DOIUrl":"10.1007/s40306-023-00509-1","url":null,"abstract":"<div><p>In this note, we give some results on maximal subextensions of plurisubharmonic functions on hyperconvex domains in <span>(mathbb C^n)</span> and introduce the notion about cone of maximal subextensions of plurisubharmonic functions. Furthermore, we establish the invariant of this cone through proper holomorphic surjections.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47294605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Note on Jacobian Problem Over (mathbb {Z}) 关于$$mathbb｛Z｝上Jacobian问题的一个注记$$
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-07-25 DOI: 10.1007/s40306-023-00504-6
Nguyen Van Chau
{"title":"A Note on Jacobian Problem Over (mathbb {Z})","authors":"Nguyen Van Chau","doi":"10.1007/s40306-023-00504-6","DOIUrl":"10.1007/s40306-023-00504-6","url":null,"abstract":"<div><p>Motivated by the Jacobian problem, this article is concerned with the density of the image set <span>(F( mathbb {Z}^n))</span> of polynomial maps <span>(Fin mathbb {Z}[X_1,dots ,X_n]^n)</span> with <span>(det DFequiv 1)</span>. It is shown that if such a map <i>F</i> is not invertible, its image set <span>(F( mathbb {Z}^n))</span> must be very thin in the lattice <span>( mathbb {Z}^n)</span>: (1) for almost all lines <i>l</i> in <span>( mathbb {Z}^n)</span> the numbers <span>(texttt {#}(F^{-1}(l) cap mathbb {Z}^n))</span> are uniformly bounded; (2) <span>(texttt {#}{ zin F( mathbb {Z}^n): vert z_ivert le B} ll B^{n-1})</span> as <span>(Brightarrow +infty )</span>, where the implicit constants depend on <i>F</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41969905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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