Results 41 to 50 of about 136,089 (106)

Efficient computation of Castelnuovo-Mumford regularity [PDF]

Mathematics of Computation, 2011
In this paper, we introduce the notion of a homogeneous ideal in quasi stable position (QSP); a new definition for the notion of generic coordinates to compute efficiently the Castelnuovo-Mumford regularity of a homogeneous ideal.
openaire   +2 more sources

Solving Degree Bounds for Iterated Polynomial Systems

IACR Transactions on Symmetric Cryptology
For Arithmetization-Oriented ciphers and hash functions Gröbner basis attacks are generally considered as the most competitive attack vector. Unfortunately, the complexity of Gröbner basis algorithms is only understood for special cases, and it is ...
Matthias Johann Steiner
doaj   +1 more source

Regularity of quasi-symbolic and bracket powers of Borel type ideals [PDF]

Romanian Journal of Mathematics and Computer Science, 2014
In this paper, we show that the regularity of the q-th quasi-symbolic power I^{((q))} and the regularity of the q-th bracket power I^{[q]} of a monomial ideal of Borel type I, satisfy the relations reg(I^{((q))})\le  q reg(I), respectively reg(I^{[q ...
Mircea Cimpoeas
doaj  

F‐purity of binomial edge ideals

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract In 2012, Matsuda introduced the class of weakly closed graphs and investigated when binomial edge ideals are F‐pure. He proved that weakly closed binomial edge ideals are F‐pure whenever the base field has positive characteristic. He conjectured that: (i) when the base field has characteristic 2, every F‐pure binomial edge ideal comes from a ...
Adam LaClair, Jason McCullough
wiley   +1 more source

Explicit constructions of short virtual resolutions of truncations

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 4000-4014, December 2025.
Abstract We propose a concept of truncation for arbitrary smooth projective toric varieties and construct explicit cellular resolutions for nef truncations of their total coordinate rings. We show that these resolutions agree with the short resolutions of Hanlon, Hicks, and Lazarev, which were motivated by symplectic geometry, and we use our definition
Lauren Cranton Heller
wiley   +1 more source

Polarization and Gorenstein liaison

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract A major open question in the theory of Gorenstein liaison is whether or not every arithmetically Cohen–Macaulay subscheme of Pn$\mathbb {P}^n$ can be G‐linked to a complete intersection. Migliore and Nagel showed that if such a scheme is generically Gorenstein (e.g., reduced), then, after re‐embedding so that it is viewed as a subscheme of Pn ...
Sara Faridi, Patricia Klein, Jenna Rajchgot, Alexandra Seceleanu   +3 more
wiley   +1 more source

GL‐algebras in positive characteristic II: The polynomial ring

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract We study GL$\mathbf {GL}$‐equivariant modules over the infinite variable polynomial ring S=k[x1,x2,…,xn,…]$S = k[x_1, x_2, \ldots, x_n, \ldots]$ with k$k$ an infinite field of characteristic p>0$p > 0$. We extend many of Sam–Snowden's far‐reaching results from characteristic zero to this setting.
Karthik Ganapathy
wiley   +1 more source

Castelnuovo-Mumford Regularity and Hyperplane Sections

Journal of Algebra, 1994
Let \(X \subset \mathbb{P}^ n\) be a projective variety and \({\mathcal I}_ X\) the ideal sheaf of \(X\) in \(\mathbb{P}^ n\). One says that \(X\) is \(k\)-regular if \(H^ i (\mathbb{P}^ n, {\mathcal I}_ X (k-i)) = 0\) for all \(i \geq 1\). The Castelnuovo-Mumford regularity \(\text{reg} (X)\) of \(X \subset \mathbb{P}^ n\) is the last such \(k ...
Hoa, L.T., Vogel, W.
openaire   +1 more source

The v-number and Castelnuovo–Mumford regularity of graphs

Journal of Algebraic Combinatorics, 2022
We prove that for every integer $k\geq 1$, there exists a connected graph $H_k$ such that $v(H_k)=reg(H_k)+k$, where $v(G)$ and $reg(G)$ denote the $v$-number and the (Castelnuovo-Mumford) regularity of a graph $G$ respectively.
openaire   +4 more sources

The weak Lefschetz property for artinian Gorenstein algebras

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3211-3222, October 2025.
Abstract It is an extremely elusive problem to determine which standard artinian graded K$K$‐algebras satisfy the weak Lefschetz property (WLP). Codimension 2 artinian Gorenstein graded K$K$‐algebras have the WLP and it is open to what extent such result might work for codimension 3 artinian Gorenstein graded K$K$‐algebras.
Rosa M. Miró‐Roig
wiley   +1 more source