Moduli of sheaves and the Chow group of K3 surfaces

By Kieran G. O’Grady. 2012

50 citations recorded by the source corpus.

Let X be a projective complex K3 surface. Beauville and Voisin singled out a 0-cycle c_X on X of degree 1: it is represented by any point lying on a rational curve in X. Huybrechts proved that the second Chern class of a rigid simple vector-bundle on X is a multiple of the Beauville-Voisin class c_X if certain hypotheses hold and he conjectured that the additional hypotheses are unnecessary. We believe that the following generalization of Huybrechts' conjecture holds. Let M and N be moduli spaces of stable pure sheaves on X (with fixed cohomological Chern characters) and suppose that they have the same dimension: then the set whose elements are second Chern classes of sheaves parametrized by the closure of M (in the corresponding moduli spaces of semistable sheaves) is equal to the set whose elements are second Chern classes of sheaves parametrized by the closure of N after a translation by a suitable multiple of c_X (so that degrees match). We will prove that the above statement holds under some additional assumptions.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/068e6941d8d33dc1085910b292c548c3c9efe821

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Remarks And Questions On Coisotropic Subvarieties and 0-Cycles of Hyper-Kähler Varieties (2015, background): “Based on the case of S where we have the results of [4], [22], [25] that concern the CH0 group of a K3 surface but will be reinterpreted in a slightly different form in Section 2, we introduce the following decreasing filtration S· on CH0(X) for any hyper-Kähler manifold”
The generalized Franchetta conjecture for some hyper-Kähler varieties, II (2020, background): “It was ﬁrst conjectured by O’Grady [O’G13] that the universal family of polarized K3 surfaces of given genus g over the corresponding moduli space satisﬁes the Franchetta property.”