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O’Grady’s birational maps and strange duality via wall-hitting

Department of Mathematics, University of Utah, 155 South 1400 East, JWB 129, Salt Lake City, Utah 84112, USA

https://doi.org/10.1142/S0129167X19500447Cited by:0 (Source: Crossref)

Abstract

We prove that O’Grady’s birational maps [K. G O’Grady, The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface, J. Algebr. Geom. 6(4) (1997) 599–644] between moduli of sheaves on an elliptic K3 surface can be interpreted as intermediate wall-crossing (wall-hitting) transformations at so-called totally semistable walls, studied by Bayer and Macrì [A. Bayer and E. Macrì, MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations, Inventiones Mathematicae 198(3) (2014) 505–590]. As a key ingredient, we describe the first totally semistable wall for ideal sheaves of $n$ $n$ points on the elliptic $K 3$ $K 3$ . As an application, we give new examples of strange duality isomorphisms, based on a result of Marian and Oprea [A. Marian and D. Oprea, Generic strange duality for K3 surfaces, with an appendix by Kota Yoshioka, Duke Math. J. 162(8) (2013) 1463–1501].

Keywords:

AMSC: 14D20, 18E30, 14J60, 14J28

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