A Sharp Vanishing Theorem for Line Bundles on K3 or Enriques Surfaces
نویسنده
چکیده
Let L be a line bundle on a K3 or Enriques surface. We give a vanishing theorem for H(L) that, unlike most vanishing theorems, gives necessary and sufficient geometrical conditions for the vanishing. This result is essential in our study of BrillNoether theory of curves on Enriques surfaces [KL1] and of Enriques-Fano threefolds [KLM].
منابع مشابه
On the number of Enriques quotients of a K3 surface
A K3 surface X is a compact complex surface with KX ∼ 0 and H (X,OX) = 0. An Enriques surface is a compact complex surface with H(Y,OY ) = H (Y,OY ) = 0 and 2KY ∼ 0. The universal covering of an Enriques surface is a K3 surface. Conversely every quotient of a K3 surface by a free involution is an Enriques surface. Here a free involution is an automorphism of order 2 without any fixed points. Th...
متن کاملGaussian Maps and Generic Vanishing I: Subvarieties of Abelian Varieties
We work with irreducible projective varieties on an algebraically closed field of any characteristic, henceforth called varieties. The contents of this paper are: (1) a general criterion expressing the vanishing of the higher cohomology of a line bundle on a Cohen-Macaulay variety in terms of a certain first-order conditions on hyperplane sections. Such conditions involve gaussian maps and the ...
متن کاملClassification of Complex Algebraic Surfaces
In this note we present the classical Enriques’ classification theorem for complex algebraic surfaces. We’ll recall basic facts about the theory of complex surfaces (structure theorems for birational maps), and discuss (using a modern (=Mori) approach) some important results like the Castelnuovo’s rationality criterion and the classification of minimal ruled surfaces. Finally, after the descrip...
متن کاملExamples of Hyperkähler Manifolds as Moduli Spaces of Sheaves on K3 Surfaces
A compact Kähler surface X is a K3 surface if it is simply connected and it carries a global homolorphic symplectic form (i.e. the canonical bundle KX ∼= OX). An example is given by the Fermat quartic: consider the degree four polynomial P (X0, ..., X3) = X 4 0 + X 4 1 + X 4 2 + X 4 3 ∈ C[X0, ..., X3]. The vanishing locus S = V (P ) is an irreducible quartic hypersurface in PC, which is simply ...
متن کاملEnriques surfaces covered by Jacobian Kummer surfaces
This paper classifies Enriques surfaces whose K3-cover is a fixed Picard-general Jacobian Kummer surface. There are exactly 31 such surfaces. We describe the free involutions which give these Enriques surfaces explicitly. As a biproduct, we show that Aut(X) is generated by elements of order 2, which is an improvement of the theorem of S. Kondo.
متن کامل