Let X be a projective complex K3 surface. Beauville and Voisin singled out a 0-cycle c(X) on X of degree 1 and Huybrechts proved that the second Chern class of a rigid simple vector-bundle on X is a multiple of cx if certain hypotheses hold. We believe that the following generalization of Huybrechts' result holds. Let M be a moduli space of stable pure sheaves on X with fixed cohomological Chem character: the set whose elements are second Chern classes of sheaves parametrized by the closure of M (in the corresponding moduli spaces of semistable sheaves) depends only on the dimension of M. We will prove that the above statement holds under some additional assumptions on the Chern character. (C) 2013 Elsevier Masson SAS. All rights reserved.
Moduli of sheaves and the Chow group of K3 surfaces / O'Grady, Kieran Gregory. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 100:5(2013), pp. 701-718. [10.1016/j.matpur.2013.01.018]
Moduli of sheaves and the Chow group of K3 surfaces
O'GRADY, Kieran Gregory
2013
Abstract
Let X be a projective complex K3 surface. Beauville and Voisin singled out a 0-cycle c(X) on X of degree 1 and Huybrechts proved that the second Chern class of a rigid simple vector-bundle on X is a multiple of cx if certain hypotheses hold. We believe that the following generalization of Huybrechts' result holds. Let M be a moduli space of stable pure sheaves on X with fixed cohomological Chem character: the set whose elements are second Chern classes of sheaves parametrized by the closure of M (in the corresponding moduli spaces of semistable sheaves) depends only on the dimension of M. We will prove that the above statement holds under some additional assumptions on the Chern character. (C) 2013 Elsevier Masson SAS. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.