×

A tour of theta dualities on moduli spaces of sheaves. (English) Zbl 1149.14301

Alexeev, Valery (ed.) et al., Curves and abelian varieties. International conference, Athens, GA, USA, March 30–April 2, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4334-5/pbk). Contemporary Mathematics 465, 175-201 (2008).
Summary: The purpose of this paper is twofold. First, we survey known results about theta dualities on moduli spaces of sheaves on curves and surfaces. Secondly, we establish new such dualities in the surface case. Among others, the case of elliptic \(K3\) surfaces is studied in detail; we propose further conjectures which are shown to imply strange duality.
For the entire collection see [Zbl 1143.14001].

MSC:

14D20 Algebraic moduli problems, moduli of vector bundles
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14H60 Vector bundles on curves and their moduli
14K25 Theta functions and abelian varieties
PDFBibTeX XMLCite
Full Text: arXiv