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Connections between algebra, combinatorics, and geometry
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In this paper, a differential graded commutative algebraic algebra was proposed for linear algebra and algebraic geometry, and the mathematical properties of the Tor algebra structure for trivariate monomial Ideals were investigated.Abstract:
Preface- Differential Graded Commutative Algebra- Secant Varieties- Fat Points and Symbolic Powers- An Introduction to Stanley-Reisner Rings- Combinatorial Resolutions- Geometric Properties of the Tor Algebra Structure for Trivariate Monomial Ideals- Interactions Between Linear Algebra and Algebraic Geometry- Fat Points- Primary Decomposition of Certain Permanental Idealsread more
Citations
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The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition
Alessandra Bernardi,Enrico Carlini,Maria Virginia Catalisano,Alessandro Gimigliano,Alessandro Oneto +4 more
TL;DR: In this article, the authors consider the problem of studying the secant varieties of a projective variety X when X is a Veronese variety, a Grassmannian or a Segre variety.
Posted Content
Second powers of cover ideals of paths
TL;DR: In this article, it was shown that the second power of the cover ideal of a path graph has linear quotients. And they constructed a recursively defined order on the generators of the ideal which yields linear quotient.
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A bound for the Waring rank of the determinant via syzygies
Mats Boij,Zach Teitler +1 more
TL;DR: In this paper, it was shown that the Waring rank of the determinant of the apolar ideal is at least $15, which was previously known to be between $14 and $18.
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On the Waring rank of binary forms: The binomial formula and a dihedral cover of rank two forms.
TL;DR: In this article, the authors considered the Waring problem for binary forms with complex coefficients and gave an explicit formula for Waring rank of any binary binomial and several examples to illustrating it.
Journal ArticleDOI
On the extremal betti numbers of squarefree monomial ideals
Luca Amata,Marilena Crupi +1 more
TL;DR: In this article, the extremal Betti numbers of a class of strongly stable ideals are studied. But the authors focus on the case where the Betti number is a polynomial ring.
References
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Journal ArticleDOI
The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition
Alessandra Bernardi,Enrico Carlini,Maria Virginia Catalisano,Alessandro Gimigliano,Alessandro Oneto +4 more
TL;DR: In this article, the authors consider the problem of studying the secant varieties of a projective variety X when X is a Veronese variety, a Grassmannian or a Segre variety.
Journal ArticleDOI
A bound for the Waring rank of the determinant via syzygies
Mats Boij,Zach Teitler +1 more
TL;DR: In this paper, it was shown that the Waring rank of the 3 × 3 determinant is at least 15, and that the symmetric cactus rank of a cactus permanent is at at least 14.
Posted Content
Second powers of cover ideals of paths
TL;DR: In this article, it was shown that the second power of the cover ideal of a path graph has linear quotients. And they constructed a recursively defined order on the generators of the ideal which yields linear quotient.
Journal ArticleDOI
Extension groups for DG modules
TL;DR: In this paper, it was shown that the Yoneda Ext-groups YExtAi(M,N) given in terms of semi-projective resolutions are not in general isomorphic to the Xoneda Extended-Gates YExtGates (M, N) given by the same authors in term of equivalence classes of extensions.
Posted Content
On the Waring rank of binary forms: The binomial formula and a dihedral cover of rank two forms.
TL;DR: In this article, the authors considered the Waring problem for binary forms with complex coefficients and gave an explicit formula for Waring rank of any binary binomial and several examples to illustrating it.