Zobrazeno 1 - 10
of 142
pro vyhledávání: '"Geramita, A. V."'
Publikováno v:
Can. J. Math.-J. Can. Math. 71 (2019) 557-578
We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible isomorphism types
Externí odkaz:
http://arxiv.org/abs/1610.06610
Let $I$ be a homogeneous ideal of $\Bbbk[x_0,\ldots,x_n]$. To compare $I^{(m)}$, the $m$-th symbolic power of $I$, with $I^m$, the regular $m$-th power, we introduce the $m$-th symbolic defect of $I$, denoted $\operatorname{sdefect}(I,m)$. Precisely,
Externí odkaz:
http://arxiv.org/abs/1610.00176
Publikováno v:
Communications in Algebra, 46:5, 2194-2204, 2018
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these ideals, and de
Externí odkaz:
http://arxiv.org/abs/1604.01101
Publikováno v:
Linear Algebra and its Applications 533:311-325 (2017)
Let $F$ be a homogeneous form of degree $d$ in $n$ variables. A Waring decomposition of $F$ is a way to express $F$ as a sum of $d^{th}$ powers of linear forms. In this paper we consider the decompositions of a form as a sum of expressions, each of w
Externí odkaz:
http://arxiv.org/abs/1511.07789
Star configurations are certain unions of linear subspaces of projective space that have been studied extensively. We develop a framework for studying a substantial generalization, which we call matroid configurations, whose ideals generalize Stanley
Externí odkaz:
http://arxiv.org/abs/1507.00380
In this paper we introduce a new method to produce lower bounds for the Waring rank of symmetric tensors. We also introduce the notion of $e$-computability and we use it to prove that Strassen's Conjecture holds in infinitely many new cases.
Com
Com
Externí odkaz:
http://arxiv.org/abs/1506.03176
Autor:
Chiantini, Luca, Geramita, Anthony V.
Let A= (a_{ij}) be a non-negative integer k x k matrix. A is a homogeneous matrix if a_{ij} + a_{kl}=a_{il} + a_{kj} for any choice of the four indexes. We ask: If A is a homogeneous matrix and if F is a form in C[x_1, \dots x_n] with deg(F) = trace(
Externí odkaz:
http://arxiv.org/abs/1503.04409
Autor:
Carlini, Enrico, Catalisano, Maria Virginia, Chiantini, Luca, Geramita, Anthony V., Woo, Youngho
In this paper we introduce the notion of $e$-computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.
Comment: The results of this paper have been
Comment: The results of this paper have been
Externí odkaz:
http://arxiv.org/abs/1502.01107
Autor:
Catalisano, M. V., Geramita, A. V., Gimigliano, A., Harbourne, B., Migliore, J., Nagel, U., Shin, Y. S.
Given the space $V={\mathbb P}^{\binom{d+n-1}{n-1}-1}$ of forms of degree $d$ in $n$ variables, and given an integer $\ell>1$ and a partition $\lambda$ of $d=d_1+\cdots+d_r$, it is in general an open problem to obtain the dimensions of the $\ell$-sec
Externí odkaz:
http://arxiv.org/abs/1502.00167
Autor:
Carlini, Enrico, Catalisano, Maria Virginia, Chiantini, Luca, Geramita, Anthony V., Woo, Youngho
In this paper we introduce the notion of linear computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.
Comment: The results of this paper have b
Comment: The results of this paper have b
Externí odkaz:
http://arxiv.org/abs/1412.2975