Spaces of quasimaps into the flag varieties and their applications
Abstract
Given a projective variety X and a smooth projective curve C one may consider the moduli space of maps C > X. This space admits certain compactification whose points are called quasimaps. In the last decade it has been discovered that in the case when X is a (partial) flag variety of a semisimple algebraic group G (or, more generally, of any symmetrizable KacMoody Lie algebra) these compactifications play an important role in such fields as geometric representation theory, geometric Langlands correspondence, geometry and topology of moduli spaces of Gbundles on algebraic surfaces, 4dimensional supersymmetric gauge theory (and probably many others). This paper is a survey of the recent results about quasimaps as well as their applications in different branches of representation theory and algebraic geometry.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2006
 DOI:
 10.48550/arXiv.math/0603454
 arXiv:
 arXiv:math/0603454
 Bibcode:
 2006math......3454B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Representation Theory
 EPrint:
 some references are corrected