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pro vyhledávání: '"Khoury, Sabine El"'
Autor:
Khoury, Sabine El, Kustin, Andrew R.
Let k be an arbitrary field, A be a standard graded Artinian Gorenstein k-algebra of embedding dimension four and socle degree three, and pi from P to A be a surjective graded homomorphism from a polynomial ring with four variables over k onto A. We
Externí odkaz:
http://arxiv.org/abs/2402.13354
This paper is concerned with finding bounds on betti numbers and describing combinatorially and topologically (minimal) free resolutions of powers of ideals generated by a fixed number $q$ of square-free monomials. Among such ideals, we focus on a sp
Externí odkaz:
http://arxiv.org/abs/2309.02644
Autor:
Khoury, Sabine El, Kustin, Andrew R.
Let $J$ be a quadratically presented grade three Gorenstein ideal in the standard graded polynomial ring $R= k[x,y,z]$, where $k$ is a field. Assume that $R/J$ satisfies the weak Lefschetz property. We give the presentation matrix for $J$ in terms of
Externí odkaz:
http://arxiv.org/abs/2206.09473
Autor:
Cooper, Susan M., Khoury, Sabine El, Faridi, Sara, Mayes-Tang, Sarah, Morey, Susan, Sega, Liana M., Spiroff, Sandra
Publikováno v:
Algebraic Combinatorics, Volume 7 (2024) no. 1, pp. 77-107
The Taylor resolution is almost never minimal for powers of monomial ideals, even in the square-free case. In this paper we introduce a smaller resolution for each power of any square-free monomial ideal, which depends only on the number of generator
Externí odkaz:
http://arxiv.org/abs/2204.03136
Autor:
Cooper, Susan M., Khoury, Sabine El, Faridi, Sara, Mayes-Tang, Sarah, Morey, Susan, Sega, Liana M., Spiroff, Sandra
This paper is concerned with the question of whether geometric structures such as cell complexes can be used to simultaneously describe the minimal free resolutions of all powers of a monomial ideal. We provide a full answer in the case of square-fre
Externí odkaz:
http://arxiv.org/abs/2108.07703
Autor:
Cooper, Susan, Khoury, Sabine El, Faridi, Sara, Mayes-Tang, Sarah, Morey, Susan, Sega, Liana M., Spiroff, Sandra
Let $I$ be a square-free monomial ideal $I$ of projective dimension one. Starting with the Taylor complex on the generators of $I^r$, we use Discrete Morse theory to describe a CW complex that supports a minimal free resolution of $I^r$. To do so, we
Externí odkaz:
http://arxiv.org/abs/2103.07959
Autor:
Cooper, Susan M., Khoury, Sabine El, Faridi, Sara, Mayes-Tang, Sarah, Morey, Susan, Şega, Liana M., Spiroff, Sandra
Given a square-free monomial ideal $I$, we define a simplicial complex labeled by the generators of $I^2$ which supports a free resolution of $I^2$. As a consequence, we obtain (sharp) upper bounds on the Betti numbers of the second power of any squa
Externí odkaz:
http://arxiv.org/abs/2103.04074
Let $R$ be a polynomial ring over a field and $M= \bigoplus_n M_n$ a finitely generated graded $R$-module, minimally generated by homogeneous elements of degree zero with a graded $R$-minimal free resolution $\mathbf{F}$. A Cohen-Macaulay module $M$
Externí odkaz:
http://arxiv.org/abs/2012.13517
Autor:
Khoury, Sabine El
Let $S$ be a polynomial ring over an algebraic closed field $k$ and $ \mathfrak p =(x,y,z,w) $ a homogeneous height four prime ideal. We give a finite characterization of the degree two component of ideals primary to $\mathfrak p$, with multiplicity
Externí odkaz:
http://arxiv.org/abs/1808.01822
Autor:
Khoury, Sabine El, Srinivasan, Hema
Let $R=S/I$ be a graded algebra with $t_i$ and $T_i$ being the minimal and maximal shifts in the minimal $S$ resolution of $R$ at degree $i$. In this paper we prove that $t_n\leq t_1+T_{n-1}$, for all $n$ and as a consequence, we show that for Gorens
Externí odkaz:
http://arxiv.org/abs/1602.02116