The Beauville-Bogomolov class as a characteristic class

Details The Beauville-Bogomolov class as a characteristic class The Beauville-Bogomolov class as a characteristic class

2011-05-16

arxiv.org/abs/1105.3223v1

Mathematics

Algebraic Geometry

33 pages

Scientific paper

Let X be any compact Kahler manifold deformation equivalent to the Hilbert scheme of length n subschemes on a K3 surface, n>1. For each point x in X we construct a rank 2n-2 reflexive coherent twisted sheaf E on X, locally free away from the point x, with the following properties. 1) E is slope-stable with respect to some Kahler class on X. 2) Set k(E):=ch(E)exp(-c_1(E)/2n-2). It is well defined, even though c_1(E) and ch(E) are not. The characteristic class k_i(E) in H^{i,i}(X) is monodromy-invariant, up to sign. Furthermore, k_i(E) can not be expressed in terms of classes of lower degree, if 1< i <= n/2. 3) The Beauville-Bogomolov class is equal to c_2(TX)+2k_2(E).

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