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Sharp bounds on Castelnuovo-Mumford regularity
Sharp bounds on Castelnuovo-Mumford regularityapplication/pdf 論文(Article) The Castelnuovo-Mumford regularity is one of the most important invariants in studying the minimal free resolution of the defining ideals of the projective varieties. There are some bounds on the Castelnuovo-Mumford regularity of the projective variety in terms of the other basic measures such as dimension, codimension and ...
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Castelnuovo–Mumford Regularity and Powers [PDF]
Commutative Algebra, 2021 This note has two goals. The first is to give a short and self contained introduction to the Castelnuovo-Mumford regularity for standard graded ring $R$ over a general base ring.
W. Bruns, A. Conca, M. Varbaro
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Castelnuovo–Mumford regularity of matrix Schubert varieties
Selecta Mathematica, 2021 Matrix Schubert varieties are affine varieties arising in the Schubert calculus of the complete flag variety. We give a formula for the Castelnuovo–Mumford regularity of matrix Schubert varieties, answering a question of Jenna Rajchgot.
O. Pechenik +2 more
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Castelnuovo–Mumford Regularity of Finite Schemes
International Mathematics Research NoticesLet $\Gamma \subset \mathbb{P}^{n}$ be a nondegenerate finite subscheme of degree $d$. It is known that the Castelnuovo–Mumford regularity $\textrm{reg} ({\Gamma })$ of $\Gamma $ is at most $\left \lceil \frac{d-n-1}{t(\Gamma )} \right \rceil +2$ where
Donghyeop Lee, Euisung Park
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Combinatorics of Castelnuovo-Mumford Regularity of Binomial Edge Ideals
Electronic Journal of Combinatorics, 2023Since the introduction of binomial edge ideals by Herzog et al. and independently Ohtani, there has been significant interest in relating algebraic invariants of the binomial edge ideal with combinatorial invariants of the underlying graph. Here, we take
A. LaClair
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Castelnuovo–Mumford Regularity of Unprojections and the Eisenbud–Goto Regularity Conjecture
International mathematics research notices, 2022McCullough and Peeva found sequences of counterexamples to the Eisenbud–Goto conjecture on the Castelnuovo–Mumford regularity by using Rees-like algebras, where entries of each sequence have increasing dimensions and codimensions.
J. Choe
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Castelnuovo–Mumford Regularity
2022For standard graded algebras over fields, Castelnuovo-Mumford regularity has become an indispensable invariant. Chapter 8 develops this notion from scratch, but in a more general version for standard graded algebras over Noetherian base rings. As in the classical case, regularity can be computed from local cohomology, minimal free resolutions and ...
Winfried Bruns +3 more
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ON THE CASTELNUOVO–MUMFORD REGULARITY OF CURVE ARRANGEMENTS
Revue Roumaine Mathematiques Pures AppliqueesThe Castelnuovo–Mumford regularity of the Jacobian algebra and of the graded module of derivations associated to a general curve arrangement in the complex projective plane are studied.
A. Dimca
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Castelnuovo–Mumford regularity of the closed neighborhood ideal of a graph
Journal of Algebraic CombinatoricsLet G be a finite simple graph, and let NI(G) denote the closed neighborhood ideal of G in a polynomial ring R. We show that if G is a forest, then the Castelnuovo–Mumford regularity of R/NI(G) is the same as the matching number of G, thus proving a ...
Shiny Chakraborty +3 more
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Non-commutative Castelnuovo–Mumford regularity
Mathematical Proceedings of the Cambridge Philosophical Society, 1999The author generalizes the notion of Castelnuovo-Mumford regularity [\textit{D. Mumford}, ``Lectures on curves on an algebraic surface'' (1966; Zbl 0187.42701)] for graded modules over non-commutative graded algebras. More exactly, the category of graded modules over quantum polynomial algebras in the sense of \textit{M. Artin} and \textit{J.-J. Zhang}
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