most recent 30 from http://mathoverflow.net 2013-05-24T12:39:39Z http://mathoverflow.net/feeds/question/10212 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/10212/moduli-spaces-of-coherent-sheaves-on-k3s Ilya Nikokoshev 2009-12-31T01:50:49Z 2009-12-31T03:03:18Z

<p>Reading 2007 paper <a href="http://arxiv.org/abs/0710.2908" rel="nofollow">A tour of theta dualities on moduli spaces of sheaves</a> by <a href="http://arxiv.org/find/math/1/au:+Marian%5FA/0/1/0/all/0/1" rel="nofollow">Alina Marian</a> and <a href="http://arxiv.org/find/math/1/au:+Oprea%5FD/0/1/0/all/0/1" rel="nofollow">Dragos Oprea</a>.</p> <blockquote> <p>Why is any moduli space of coherent sheaves on a K3 surface deformation equivalent to a moduli space of sheaves on an elliptic K3?</p> </blockquote> <p>(The authors consider a space of "Gieseker H-semistable sheaves", if that is important)</p>

http://mathoverflow.net/questions/10212/moduli-spaces-of-coherent-sheaves-on-k3s/10220#10220 Tony Pantev 2009-12-31T03:03:18Z 2009-12-31T03:03:18Z

<p>This follows from a result of Yoshioka. In Theorem 8.1 of this <a href="http://arxiv.org/abs/math/0009001" rel="nofollow">paper</a> Yoshioka showed that every moduli space of coherent sheaves on a K3 surface $X$ is deformation equivalent to an appropriate Hilbert scheme of points of $X$. Since every K3 is deformation equivalent to an elliptic K3 it follows that their Hilbert schemes are deformation equivalent and so you get the statement that you wanted.</p>