Results 51 to 60 of about 3,151 (106)
Non-commutative Castelnuovo–Mumford regularity and AS-regular algebras
Journal of Algebra, 2009 Let $A$ be a connected graded $k$-algebra with a balanced dualizing complex. We prove that $A$ is a Koszul AS-regular algebra if and only if that the Castelnuovo-Mumford regularity and the Ext-regularity coincide for all finitely generated $A$-modules. This can be viewed as a non-commutative version of \cite[Theorem 1.3]{ro}.
Dong, Z.-C., Wu, Q.-S.
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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 +3 more
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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
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
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Weighted Castelnuovo–Mumford regularity and weighted global generation [PDF]
Journal of Algebra and Its Applications, 2019 We introduce and study a notion of Castelnuovo–Mumford regularity suitable for weighted projective spaces.
Malaspina, F., Sankaran, G. K.
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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
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Castelnuovo–Mumford regularity bounds for singular surfaces [PDF]
Mathematische Zeitschrift, 2015 We prove the regularity conjecture, namely Eisenbud-Goto conjecture, for a normal surface with rational, Gorenstein elliptic and log canonical singularities. Along the way, we bound the regularity for a dimension zero scheme by its Loewy length and for a curve allowing embedded or isolated point components by its arithmetic degree.
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Algebraic invariants of edge ideals from strong products of paths and cycles
AIMS MathematicsThis paper investigates algebraic invariants of edge ideals associated with families of graphs constructed as the strong product of a path or cycle with the complete graph $ K_m $, namely $ \mathscr{P}_\gamma = P_\gamma \boxtimes K_m $ and $ \mathscr{C}_\
Ahtsham Ul Haq +2 more
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Rational normal curves in weighted projective space
Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2816-2837, September 2025.Abstract This article aims to extend classical homological results about the rational normal curves to analogues in weighted projective spaces. Results include determinantality and nonstandard versions of quadratic generation and the Koszul property.
Caitlin M. Davis, Aleksandra Sobieska
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Veronese transform, and Castelnuovo-Mumford regularity of modules
, 2016 International audienceVeronese rings, Segre embeddings or more generally Segre-Veronese embeddings are very important rings in Algebraic Geometry. In this paper we present an original, elementary way to compute the Hilbert-Poincare series of these rings,
Morales, Marcel, Nguyen Thi, Dung
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