m-Blocks Collections and Castelnuovo-mumford Regularity in multiprojective spaces
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چکیده
منابع مشابه
m-BLOCKS COLLECTIONS AND CASTELNUOVO-MUMFORD REGULARITY IN MULTIPROJECTIVE SPACES
The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on n-dimensional smooth projective varieties X with an n-block collection B which generates the bounded derived category Db(OX -mod). To this end, we use the theory of n-blocks and Beilinson type spectral sequence to define the notion of regularity of a cohere...
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We define the concept of regularity for bigraded modules over a bigraded polynomial ring. In this setting we prove analogs of some of the classical results on m-regularity for graded modules over polynomial algebras.
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We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the m...
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The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given an approximation by modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the m...
متن کامل, Castelnuovo - Mumford Regularity , and Generic Initial Ideals
KOSZUL ALGEBRAS, CASTELNUOVO-MUMFORD REGULARITY, AND GENERIC INITIAL IDEALS Giulio Caviglia The University of Kansas Advisor: Craig Huneke August, 2004 The central topics of this dissertation are: Koszul Algebras, bounds for the Castelnuovo Mumford regularity, and methods involving the use of generic changes of coordinates and generic hyperplane restrictions. We give an introduction to Koszul a...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 2007
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000009387