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Tangential Weak Defectiveness and Generic Identifiability 切向弱缺陷与一般可识别性
arXiv: Algebraic Geometry Pub Date : 2020-09-02 DOI: 10.1093/IMRN/RNAB091
Alex Casarotti, M. Mella
{"title":"Tangential Weak Defectiveness and Generic Identifiability","authors":"Alex Casarotti, M. Mella","doi":"10.1093/IMRN/RNAB091","DOIUrl":"https://doi.org/10.1093/IMRN/RNAB091","url":null,"abstract":"We investigate the uniqueness of decomposition of general tensors $Tin {mathbb C}^{n_1+1}otimescdotsotimes{mathbb C}^{n_r+1}$ as a sum of tensors of rank $1$. This is done extending the theory developed in a previous paper by the second author to the framework of non twd varieties. In this way we are able to prove the non generic identifiability of infinitely many partially symmetric tensors.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"149 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121771669","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: 5
Projective plane curves whose automorphism groups are simple and primitive 自同构群为简单原始的射影平面曲线
arXiv: Algebraic Geometry Pub Date : 2020-08-31 DOI: 10.2996/kmj44208
Yusuke Yoshida
{"title":"Projective plane curves whose automorphism groups are simple and primitive","authors":"Yusuke Yoshida","doi":"10.2996/kmj44208","DOIUrl":"https://doi.org/10.2996/kmj44208","url":null,"abstract":"We study complex projective plane curves with a given group of automorphisms. Let $G$ be a simple primitive subgroup of $PGL(3, mathbb{C})$, which is isomorphic to $A_{6}$, $A_{5}$ or $PSL(2, mathbb{F}_{7})$. We obtain a necessary and sufficient condition on $d$ for the existence of a nonsingular projective plane curve of degree $d$ invariant under $G$. We also study an analogous problem on integral curves.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123828870","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: 3
A note on finite determinacy of matrices 关于矩阵有限确定性的一个注记
arXiv: Algebraic Geometry Pub Date : 2020-08-30 DOI: 10.4310/pamq.2020.v16.n4.a10
Thuy Huong Pham, P. Marques
{"title":"A note on finite determinacy of matrices","authors":"Thuy Huong Pham, P. Marques","doi":"10.4310/pamq.2020.v16.n4.a10","DOIUrl":"https://doi.org/10.4310/pamq.2020.v16.n4.a10","url":null,"abstract":"In this note, we give a necessary and sufficient condition for a matrix A in M to be finitely G-determined, where M is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M by change of coordinates together with multiplication by invertible matrices from both sides.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132282146","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
Numerical homotopies from Khovanskii bases Khovanskii基的数值同伦
arXiv: Algebraic Geometry Pub Date : 2020-08-29 DOI: 10.1090/mcom/3689
M. Burr, F. Sottile, Elise Walker
{"title":"Numerical homotopies from Khovanskii bases","authors":"M. Burr, F. Sottile, Elise Walker","doi":"10.1090/mcom/3689","DOIUrl":"https://doi.org/10.1090/mcom/3689","url":null,"abstract":"We present numerical homotopy continuation algorithms for solving systems of equations on a variety in the presence of a finite Khovanskii basis. These take advantage of Anderson's flat degeneration to a toric variety. When Anderson's degeneration embeds into projective space, our algorithm is a special case of a general toric two-step homotopy algorithm. When Anderson's degeneration is embedded in a weighted projective space, we explain how to lift to a projective space and construct an appropriate modification of the toric homotopy. Our algorithms are illustrated on several examples using Macaulay2.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133210546","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: 8
Left Demazure–Lusztig Operators on Equivariant (Quantum) Cohomology and K-Theory 等变(量子)上同调和k理论上的左demazur - lusztig算子
arXiv: Algebraic Geometry Pub Date : 2020-08-28 DOI: 10.1093/IMRN/RNAB049
L. Mihalcea, H. Naruse, C. Su
{"title":"Left Demazure–Lusztig Operators on Equivariant (Quantum) Cohomology and K-Theory","authors":"L. Mihalcea, H. Naruse, C. Su","doi":"10.1093/IMRN/RNAB049","DOIUrl":"https://doi.org/10.1093/IMRN/RNAB049","url":null,"abstract":"We study the Demazure-Lusztig operators induced by the left multiplication on partial flag manifolds $G/P$. We prove that they generate the Chern-Schwartz-MacPherson classes of Schubert cells (in equivariant cohomology), respectively their motivic Chern classes (in equivariant K theory), in any partial flag manifold. Along the way we advertise many properties of the left and right divided difference operators in cohomology and K theory, and their actions on Schubert classes. We apply this to construct left divided difference operators in equivariant quantum cohomology, and equivariant quantum K theory, generating Schubert classes, and satisfying a Leibniz rule compatible with the quantum product.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123380418","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: 17
Seshadri constants on abelian and bielliptic surfaces–Potential values and lower bounds 阿贝尔曲面和双椭圆曲面上的Seshadri常数。势值和下界
arXiv: Algebraic Geometry Pub Date : 2020-08-17 DOI: 10.1090/proc/15893
Thomas Bauer, L. Farnik
{"title":"Seshadri constants on abelian and bielliptic surfaces–Potential values and lower bounds","authors":"Thomas Bauer, L. Farnik","doi":"10.1090/proc/15893","DOIUrl":"https://doi.org/10.1090/proc/15893","url":null,"abstract":"In this note we contribute to the study of Seshadri constants on abelian and bielliptic surfaces. We specifically focus on bounds that hold on all such surfaces, depending only on the self-intersection of the ample line bundle under consideration. Our result improves previous bounds and it provides rational numbers as bounds, which are potential Seshadri constants.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121751104","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 Torelli theorem for moduli spaces of parabolic vector bundles over an elliptic curve 椭圆曲线上抛物向量束模空间的Torelli定理
arXiv: Algebraic Geometry Pub Date : 2020-08-12 DOI: 10.1090/proc/15937
T. Fassarella, Luana Justo
{"title":"A Torelli theorem for moduli spaces of parabolic vector bundles over an elliptic curve","authors":"T. Fassarella, Luana Justo","doi":"10.1090/proc/15937","DOIUrl":"https://doi.org/10.1090/proc/15937","url":null,"abstract":"Let $C$ be an elliptic curve, $win C$, and let $Ssubset C$ be a finite subset of cardinality at least $3$. We prove a Torelli type theorem for the moduli space of rank two parabolic vector bundles with determinant line bundle $mathcal O_C(w)$ over $(C,S)$ which are semistable with respect to a weight vector $big(frac{1}{2}, dots, frac{1}{2}big)$.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124833551","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: 1
Frobenius-Witt differentials and regularity. Frobenius-Witt微分和正则性。
arXiv: Algebraic Geometry Pub Date : 2020-08-10 DOI: 10.2140/ant.2022.16.369
Takeshi Saito
{"title":"Frobenius-Witt differentials and regularity.","authors":"Takeshi Saito","doi":"10.2140/ant.2022.16.369","DOIUrl":"https://doi.org/10.2140/ant.2022.16.369","url":null,"abstract":"T. Dupuy, E. Katz, J. Rabinoff, D. Zureick-Brown introduced the module of total $p$-differentials for a ring over $Z/p^2Z$. We study the same construction for a ring over $Z_{(p)}$ and prove a regularity criterion. For a local ring, the tensor product with the residue field is constructed in a different way by O. Gabber, L. Ramero. In another article arXiv:2006.00448, we use the sheaf of FW-differentials to define the cotangent bundle and the micro-support of an etale sheaf.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114152450","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: 3
Brill-Noether special cubic fourfolds of discriminant 14 Brill-Noether特殊三次四重判别14
arXiv: Algebraic Geometry Pub Date : 2020-07-30 DOI: 10.1017/9781108877831.002
Asher Auel
{"title":"Brill-Noether special cubic fourfolds of discriminant 14","authors":"Asher Auel","doi":"10.1017/9781108877831.002","DOIUrl":"https://doi.org/10.1017/9781108877831.002","url":null,"abstract":"We study the Brill-Noether theory of curves on K3 surfaces that are Hodge theoretically associated to cubic fourfolds of discriminant 14. We prove that any smooth curve in the polarization class has maximal Clifford index and deduce that a cubic fourfold contains disjoint planes if and only if it admits a Brill-Noether special associated K3 surface of degree 14. As an application, the complement of the pfaffian locus, inside the Noether-Lefschetz divisor of discriminant 14 in the moduli space of cubic fourfolds, is contained in the irreducible locus of cubic fourfolds containing two disjoint planes.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130402810","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: 5
Families of Gröbner Degenerations, Grassmannians and Universal Cluster Algebras Gröbner退化、格拉斯曼代数和泛簇代数族
arXiv: Algebraic Geometry Pub Date : 2020-07-29 DOI: 10.3842/SIGMA.2021.059
L. Bossinger, F. Mohammadi, Alfredo N'ajera Ch'avez
{"title":"Families of Gröbner Degenerations, Grassmannians and Universal Cluster Algebras","authors":"L. Bossinger, F. Mohammadi, Alfredo N'ajera Ch'avez","doi":"10.3842/SIGMA.2021.059","DOIUrl":"https://doi.org/10.3842/SIGMA.2021.059","url":null,"abstract":"Let $V$ be the weighted projective variety defined by a weighted homogeneous ideal $J$ and $C$ a maximal cone in the Grobner fan of $J$ with $m$ rays. We construct a flat family over $mathbb A^m$ that assembles the Grobner degenerations of $V$ associated with all faces of $C$. This is a multi-parameter generalization of the classical one-parameter Grobner degeneration associated to a weight. We show that our family can be constructed from Kaveh-Manon's recent work on the classification of toric flat families over toric varieties: it is the pullback of a toric family defined by a Rees algebra with base $X_C$ (the toric variety associated to $C$) along the universal torsor $mathbb A^m to X_C$. \u0000We apply this construction to the Grassmannians ${rm Gr}(2,mathbb C^n)$ with their Plucker embeddings and the Grassmannian ${rm Gr}(3,mathbb C^6)$ with its cluster embedding. In each case there exists a unique maximal Grobner cone whose associated initial ideal is the Stanley-Reisner ideal of the cluster complex. We show that the corresponding cluster algebra with universal coefficients arises as the algebra defining the flat family associated to this cone. Further, for ${rm Gr}(2,mathbb C^n)$ we show how Escobar-Harada's mutation of Newton-Okounkov bodies can be recovered as tropicalized cluster mutation.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130085817","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: 24
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