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Collectanea Mathematica最新文献

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On reduction numbers and Castelnuovo–Mumford regularity of blowup rings and modules 关于炸环和模块的还原数和卡斯特诺沃-蒙福德正则性
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-03-07 DOI: 10.1007/s13348-024-00436-w
Cleto B. Miranda-Neto, Douglas S. Queiroz
{"title":"On reduction numbers and Castelnuovo–Mumford regularity of blowup rings and modules","authors":"Cleto B. Miranda-Neto, Douglas S. Queiroz","doi":"10.1007/s13348-024-00436-w","DOIUrl":"https://doi.org/10.1007/s13348-024-00436-w","url":null,"abstract":"<p>We prove new results on the interplay between reduction numbers and the Castelnuovo–Mumford regularity of blowup algebras and blowup modules, the key basic tool being the operation of Ratliff–Rush closure. First, we answer in two particular cases a question of M. E. Rossi, D. T. Trung, and N. V. Trung about Rees algebras of ideals in two-dimensional Buchsbaum local rings, and we even ask whether one of such situations always holds. In another theorem we largely generalize a result of A. Mafi on ideals in two-dimensional Cohen–Macaulay local rings, by extending it to arbitrary dimension (and allowing for the setting relative to a Cohen–Macaulay module). We derive a number of applications, including a characterization of (polynomial) ideals of linear type, progress on the theory of generalized Ulrich ideals, and improvements of results by other authors.\u0000</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140076275","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
New insights on slant submanifolds in almost Hermitian geometry 关于几乎赫米蒂几何中斜面子曼形体的新见解
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-02-13 DOI: 10.1007/s13348-024-00432-0
Adara M. Blaga
{"title":"New insights on slant submanifolds in almost Hermitian geometry","authors":"Adara M. Blaga","doi":"10.1007/s13348-024-00432-0","DOIUrl":"https://doi.org/10.1007/s13348-024-00432-0","url":null,"abstract":"<p>We provide the necessary and sufficient condition for a pointwise slant submanifold with respect to two anti-commuting almost Hermitian structures to be also pointwise slant with respect to a family of almost Hermitian structures generated by them. On the other hand, we show that the property of being pointwise slant is transitive on a class of proper pointwise slant immersed submanifolds of almost Hermitian manifolds. We illustrate the results with suitable examples.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760714","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
Identifiability and singular locus of secant varieties to Grassmannians 格拉斯曼矢切变种的可识别性和奇异位点
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-01-06 DOI: 10.1007/s13348-023-00429-1
Vincenzo Galgano, Reynaldo Staffolani
{"title":"Identifiability and singular locus of secant varieties to Grassmannians","authors":"Vincenzo Galgano, Reynaldo Staffolani","doi":"10.1007/s13348-023-00429-1","DOIUrl":"https://doi.org/10.1007/s13348-023-00429-1","url":null,"abstract":"<p>Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematic areas. Grassmannians are the building blocks for skewsymmetric tensors. Although they are ubiquitous in the literature, the geometry of their secant varieties is not completely understood. In this work we determine the singular locus of the secant variety of lines to a Grassmannian <i>Gr</i>(<i>k</i>, <i>V</i>) using its structure as <span>({{,textrm{SL},}}(V))</span>-variety. We solve the problems of identifiability and tangential-identifiability of points in the secant variety: as a consequence, we also determine the second Terracini locus to a Grassmannian.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373479","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 the depth of simplicial affine semigroup rings 论简单仿射半群环的深度
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-01-02 DOI: 10.1007/s13348-023-00424-6
Raheleh Jafari, Ignacio Ojeda
{"title":"On the depth of simplicial affine semigroup rings","authors":"Raheleh Jafari, Ignacio Ojeda","doi":"10.1007/s13348-023-00424-6","DOIUrl":"https://doi.org/10.1007/s13348-023-00424-6","url":null,"abstract":"<p>We recall and delve into the different characterizations of the depth of an affine semigroup ring, providing an original characterization of depth two in three and four dimensional cases which are closely related to the existence of a maximal element in certain Apéry sets.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093056","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
Stable trace ideals and applications. 稳定轨迹理想及其应用
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2024-01-01 Epub Date: 2023-02-08 DOI: 10.1007/s13348-023-00391-y
Hailong Dao, Haydee Lindo
{"title":"Stable trace ideals and applications.","authors":"Hailong Dao, Haydee Lindo","doi":"10.1007/s13348-023-00391-y","DOIUrl":"10.1007/s13348-023-00391-y","url":null,"abstract":"<p><p>We study stable trace ideals in one dimensional local Cohen-Macaulay rings and give numerous applications.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10973018/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44095863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lorentzian connections with parallel twistor-free torsion 具有平行无扭的洛伦兹连接
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2023-12-30 DOI: 10.1007/s13348-023-00430-8
Igor Ernst, Anton S. Galaev
{"title":"Lorentzian connections with parallel twistor-free torsion","authors":"Igor Ernst, Anton S. Galaev","doi":"10.1007/s13348-023-00430-8","DOIUrl":"https://doi.org/10.1007/s13348-023-00430-8","url":null,"abstract":"<p>We describe Lorentzian manifolds that admit metric connections with parallel torsion having zero twistorial component and non-zero vectorial component. We also describe Lorentzian manifolds admitting metric connections with closed parallel skew-symmetric torsion.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139063534","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
Stability of standard Einstein metrics on homogeneous spaces of non-simple Lie groups 非简单李群同质空间上标准爱因斯坦度量的稳定性
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2023-12-28 DOI: 10.1007/s13348-023-00431-7
Valeria Gutiérrez, Jorge Lauret
{"title":"Stability of standard Einstein metrics on homogeneous spaces of non-simple Lie groups","authors":"Valeria Gutiérrez, Jorge Lauret","doi":"10.1007/s13348-023-00431-7","DOIUrl":"https://doi.org/10.1007/s13348-023-00431-7","url":null,"abstract":"<p>The classification of compact homogeneous spaces of the form <span>(M=G/K)</span>, where <i>G</i> is a non-simple Lie group, such that the standard metric is Einstein is still open. The only known examples are 4 infinite families and 3 isolated spaces found by Nikonorov and Rodionov in the 90 s. In this paper, we prove that most of these standard Einstein metrics are unstable as critical points of the scalar curvature functional on the manifold of all unit volume <i>G</i>-invariant metrics on <i>M</i>, providing a lower bound for the coindex in the case of Ledger–Obata spaces. On the other hand, examples of stable (in particular, local maxima) invariant Einstein metrics on certain homogeneous spaces of non-simple Lie groups are also given.\u0000</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139063309","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 Grayson-type theorem for star-shaped curves 星形曲线的格雷森型定理
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2023-12-11 DOI: 10.1007/s13348-023-00425-5
Jianbo Fang, Yunlong Yang, Fangwei Chen
{"title":"A Grayson-type theorem for star-shaped curves","authors":"Jianbo Fang, Yunlong Yang, Fangwei Chen","doi":"10.1007/s13348-023-00425-5","DOIUrl":"https://doi.org/10.1007/s13348-023-00425-5","url":null,"abstract":"<p>This paper focuses on a length-preserving flow for star-shaped curves with respect to the origin. Under the length-preserving flow, the evolving curve keeps star-shapedness and converges smoothly to a circle, which can be regarded as a Grayson-type theorem for star-shaped curves under this flow.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138568086","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
Cox rings of blow-ups of multiprojective spaces 多射空间吹胀的考克斯环
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2023-12-07 DOI: 10.1007/s13348-023-00428-2
Michele Bolognesi, Alex Massarenti, Elena Poma
{"title":"Cox rings of blow-ups of multiprojective spaces","authors":"Michele Bolognesi, Alex Massarenti, Elena Poma","doi":"10.1007/s13348-023-00428-2","DOIUrl":"https://doi.org/10.1007/s13348-023-00428-2","url":null,"abstract":"<p>Let <span>(X^{1,n}_r)</span> be the blow-up of <span>(mathbb {P}^1times mathbb {P}^n)</span> in <i>r</i> general points. We describe the Mori cone of <span>(X^{1,n}_r)</span> for <span>(rle n+2)</span> and for <span>(r = n+3)</span> when <span>(nle 4)</span>. Furthermore, we prove that <span>(X^{1,n}_{n+1})</span> is log Fano and give an explicit presentation for its Cox ring.\u0000</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547705","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
Fujita exponent on stratified Lie groups 分层李群上的Fujita指数
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2023-12-01 DOI: 10.1007/s13348-023-00427-3
Durvudkhan Suragan, Bharat Talwar
{"title":"Fujita exponent on stratified Lie groups","authors":"Durvudkhan Suragan, Bharat Talwar","doi":"10.1007/s13348-023-00427-3","DOIUrl":"https://doi.org/10.1007/s13348-023-00427-3","url":null,"abstract":"<p>We prove that <span>(frac{Q}{Q-2})</span> is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension <i>Q</i>. This covers the Euclidean case and gives new insight into proof techniques on nilpotent Lie groups. The equation we study has a forcing term which depends only upon the group elements and has positive integral. The stratified Lie group structure plays an important role in our proofs, along with test function method and Banach fixed point theorem.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538927","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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