Zobrazeno 1 - 10
of 89
pro vyhledávání: '"Geramita, Anthony 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
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:
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
We describe the graded characters and Hilbert functions of certain graded artinian Gorenstein quotients of the polynomial ring which are also representations of the symmetric group. Specifically, we look at those algebras whose socles are trivial rep
Externí odkaz:
http://arxiv.org/abs/1407.7228
Let $\lambda =[d_1,\dots,d_r]$ be a partition of $d$. Consider the variety $\mathbb{X}_{2,\lambda} \subset \mathbb{P}^N$, $N={d+2 \choose 2}-1$, parameterizing forms $F\in k[x_0,x_1,x_2]_d$ which are the product of $r\geq 2$ forms $F_1,\dots,F_r$, wi
Externí odkaz:
http://arxiv.org/abs/1404.3911
In this paper we consider the problem of determining the Hilbert function of schemes X of the proiective space P^n which are the generic union of s lines and one m-multiple point. We completely solve this problem for any s and m when n > 3. When n=3
Externí odkaz:
http://arxiv.org/abs/1308.6796