Koszul spaces
نویسندگان
چکیده
منابع مشابه
Sheaves on Triangulated Spaces and Koszul Duality
Let X be a finite connected simplicial complex, and let δ be a perversity (i.e., some function from integers to integers). One can consider two categories: (1) the category of perverse sheaves cohomologically constructible with respect to the triangulation, and (2) the category of sheaves constant along the perverse simplices (δ-sheaves). We interpret the categories (1) and (2) as categories of...
متن کاملKoszul Configurations of Points in Projective Spaces
We prove a new criterion for the homogeneous coordinate ring of a finite set of points in Pn to be Koszul. Like the well known criterion due to Kempf [7] it involves only incidence conditions on linear spans of subsets of a given set. We also give a sufficient condition for the Koszul property to be preserved when passing to a subset of a finite set of points in Pn.
متن کاملKoszul Divisors on Moduli Spaces of Curves
In this paper we describe a general method of constructing special effective divisors on various moduli spaces using the syzygies of the parametrized objects. The method can be applied to a wide range of moduli problems with the property that the coarse moduli space has canonical singularities hence pluricanonical forms extend over any desingularization of the moduli space. Here we treat the ca...
متن کاملDescribing Coherent Sheaves on Projective Spaces via Koszul Duality
It is well known that there is a close connection between coherent sheaves on a projective space P(V ) where V is a a vector space over a field k, and finitely generated graded modules over the symmetric algebra S(V ). The Bernstein-Gelfand-Gelfand (BGG) correspondence [5] from 1978 relates coherent sheaves on P(V ) with graded modules over the exterior algebra Λ(V ∗) = ⊕Λi(V ∗) where V ∗ is th...
متن کاملKOSZUL DIVISORS ON MODULI SPACES OF CURVES By GAVRIL FARKAS
Given a moduli space, how can one construct the “best” (in the sense of higher dimensional algebraic geometry) effective divisor on it? We show that, at least in the case of the moduli space of curves, the answer is provided by the Koszul divisor defined in terms of the syzygies of the parameterized objects. In this paper, we find a formula for the slopes of all Koszul divisors on Mg. In partic...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2014
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2014-05935-7