Sn-equivariant sheaves and Koszul cohomology
نویسنده
چکیده
Background The Koszul cohomology of a line bundle L on an algebraic variety X was introduced by Green in [1]. Koszul cohomology is very closely related to the syzygies of the embedding defined by L (if L is very ample) and is thus related to a host of classical questions. We assume that the reader is already aware of these relations and the main theorems on Koszul cohomology; for a detailed discussion, the reader is referred to [1]. Recently, in [2], it was realized that a conjectural uniform asymptotic picture emerges as L becomes more positive. We give a new interpretation of Koszul cohomology which we believe will clarify this picture. As an application, we prove that Kp,q(B, dA+ P) grows polynomially in d. In particular, this gives a partial answer to Problem 7.2 from [2]. More precisely, we establish.
منابع مشابه
Equivariant cohomology, Koszul duality, and the localization theorem
(1.1) This paper concerns three aspects of the action of a compact group K on a space X . The ®rst is concrete and the others are rather abstract. (1) Equivariantly formal spaces. These have the property that their cohomology may be computed from the structure of the zero and one dimensional orbits of the action of a maximal torus in K. (2) Koszul duality. This enables one to translate facts ab...
متن کاملGraph Homology: Koszul and Verdier Duality
We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology of both the commutative and Lie types in computations of the cohomology of the outer automorphism group of a free group. Another consequence is an explicit co...
متن کاملWeights in the cohomology of toric varieties
We describe the weight filtration in the cohomology of toric varieties. We present the role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We also obtain a results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complex IH∗ T (X)⊗ H ∗(T ).
متن کاملRing structures of mod p equivariant cohomology rings and ring homomorphisms between them
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...
متن کاملVanishing of Odd Dimensional Intersection Cohomology Ii
For a variety where a connected linear algebraic group acts with only finitely many orbits, each of which admits an attractive slice, we show that the stratification by orbits is perfect for equivariant intersection cohomology with respect to any equivariant local system. This applies to provide a relationship between the vanishing of the odd dimensional intersection cohomology sheaves and of t...
متن کامل