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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":"1 1","pages":""},"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":"6 1","pages":""},"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
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":"29 1","pages":""},"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":"3 1","pages":""},"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":"44 1","pages":""},"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":"77 1","pages":""},"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":"29 1","pages":""},"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
Infinitely many positive energy solutions for semilinear Neumann equations with critical Sobolev exponent and concave-convex nonlinearity 具有临界Sobolev指数和凹凸非线性的半线性Neumann方程的无穷多正能量解
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2023-11-29 DOI: 10.1007/s13348-023-00426-4
Rachid Echarghaoui, Rachid Sersif, Zakaria Zaimi
{"title":"Infinitely many positive energy solutions for semilinear Neumann equations with critical Sobolev exponent and concave-convex nonlinearity","authors":"Rachid Echarghaoui, Rachid Sersif, Zakaria Zaimi","doi":"10.1007/s13348-023-00426-4","DOIUrl":"https://doi.org/10.1007/s13348-023-00426-4","url":null,"abstract":"<p>The authors of Cao and Yan (J Differ Equ 251:1389–1414, 2011) have considered the following semilinear critical Neumann problem </p><span>$$begin{aligned} varvec{-Delta u=vert uvert ^{2^{*}-2} u+g(u) quad text{ in } Omega , quad frac{partial u}{partial nu }=0 quad text{ on } partial Omega ,} end{aligned}$$</span><p>where <span>(varvec{Omega })</span> is a bounded domain in <span>(varvec{mathbb {R}^{N}})</span> satisfying some geometric conditions, <span>(varvec{nu })</span> is the outward unit normal of <span>(varvec{partial Omega , 2^{*}:=frac{2 N}{N-2}})</span> and <span>(varvec{g(t):=mu vert tvert ^{p-2} t-t,})</span> where <span>(varvec{p in left( 2,2^{*}right) })</span> and <span>(varvec{mu &gt;0})</span> are constants. They proved the existence of infinitely many solutions with positive energy for the above problem if <span>(varvec{N&gt;max left( frac{2(p+1)}{p-1}, 4right) .})</span> In this present paper, we consider the case where the exponent <span>(varvec{p in left( 1,2right) })</span> and we show that if <span>(varvec{N&gt;frac{2(p+1)}{p-1},})</span> then the above problem admits an infinite set of solutions with positive energy. Our main result extend that obtained by P. Han in [9] for the case of elliptic problem with Dirichlet boundary conditions.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":"25 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538890","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
Maximal operators on hyperbolic triangles 双曲三角形上的极大算子
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2023-11-25 DOI: 10.1007/s13348-023-00419-3
Romain Branchereau, Samuel Bronstein, Anthony Gauvan
{"title":"Maximal operators on hyperbolic triangles","authors":"Romain Branchereau, Samuel Bronstein, Anthony Gauvan","doi":"10.1007/s13348-023-00419-3","DOIUrl":"https://doi.org/10.1007/s13348-023-00419-3","url":null,"abstract":"<p>We characterize the boundedness properties on the spaces <span>(L^p( mathbb {H}^2))</span> of the maximal operator <span>(M_mathcal {B})</span> where <span>(mathcal {B})</span> is an arbitrary family of hyperbolic triangles stable by isometries. </p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":"11 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538920","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
Cofiniteness of local cohomology modules and subcategories of modules 局部上同调模及其子范畴的共性
IF 1.1 2区 数学
Collectanea Mathematica Pub Date : 2023-11-21 DOI: 10.1007/s13348-023-00416-6
Ryo Takahashi, Naoki Wakasugi
{"title":"Cofiniteness of local cohomology modules and subcategories of modules","authors":"Ryo Takahashi, Naoki Wakasugi","doi":"10.1007/s13348-023-00416-6","DOIUrl":"https://doi.org/10.1007/s13348-023-00416-6","url":null,"abstract":"<p>Let <i>R</i> be a commutative noetherian ring and <i>I</i> an ideal of <i>R</i>. Assume that for all integers <i>i</i> the local cohomology module <span>({text {H}}_I^i(R))</span> is <i>I</i>-cofinite. Suppose that <span>(R_mathfrak {p})</span> is a regular local ring for all prime ideals <span>(mathfrak {p})</span> that do not contain <i>I</i>. In this paper, we prove that if the <i>I</i>-cofinite modules form an abelian category, then for all finitely generated <i>R</i>-modules <i>M</i> and all integers <i>i</i>, the local cohomology module <span>({text {H}}_I^i(M))</span> is <i>I</i>-cofinite.\u0000</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":"292 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538921","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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