Arend Bayer : Projectivity and birational geometry of Bridgeland moduli spaces

Posted by Artie Prendergast-Smith , part of the Algebraic Geometry Seminar.

At

Feb. 15, 2012, 5 p.m.

In

SEO 427

Abstract

I will present a construction of a nef divisor for every moduli space of Bridgeland stable complexes on an algebraic variety. In the case of K3 surfaces, we can use it to prove projectivity of the moduli space, generalizing a result of Minamide, Yanagida and Yoshioka. Its dependence on the stability condition gives a systematic explanation for the compatibility of wall-crossing of the moduli space with its birational transformations; this phenomenon had first been observed by Arcara-Bertram. This is based on joint work with Emanuele Macrì.