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On some moduli spaces of bundles on $K3$ surfaces, II


Author: C. G. Madonna
Journal: Proc. Amer. Math. Soc. 140 (2012), 3397-3408
MSC (2010): Primary 14D20, 14J28
DOI: https://doi.org/10.1090/S0002-9939-2012-11251-1
Published electronically: February 23, 2012
MathSciNet review: 2929009
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Abstract: We give several examples of the existence of infinitely many divisorial conditions on the moduli space of polarized $K3$ surfaces $(S,H)$ of degree $H^2=2g-2$, $g \geq 3$, and Picard number $\rho (S)=rk N(S)=2$, such that for a general $K3$ surface $S$ satisfying these conditions the moduli space of sheaves $M_S(r,H,s)$ is birationally equivalent to the Hilbert scheme $S[g-rs]$ of zero-dimensional subschemes of $S$ of length equal to $g-rs$. This result generalizes a result of Nikulin when $g=rs+1$ and an earlier result of the author when $r=s=2$, $g \geq 5$.


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Additional Information

C. G. Madonna
Affiliation: Faculty of Teacher Training and Education, Autonoma University of Madrid, Campus de Cantoblanco, C/Fco. Tomas y Valiente 3, Madrid E-28049, Spain
Email: carlo.madonna@uam.es

Received by editor(s): August 17, 2010
Received by editor(s) in revised form: April 12, 2011
Published electronically: February 23, 2012
Additional Notes: The author was supported by EPSRC grant EP/D061997/1. The author is a member of project MTM2007-67623, founded by the Spanish MEC
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.