Spaces of quasi-maps 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 quasi-maps. In the last decade it has been discovered that in the case when X is a (partial) flag variety of a semi-simple algebraic group G (or, more generally, of any symmetrizable Kac-Moody 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 G-bundles on algebraic surfaces, 4-dimensional super-symmetric gauge theory (and probably many others). This paper is a survey of the recent results about quasi-maps as well as their applications in different branches of representation theory and algebraic geometry.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- March 2006
- DOI:
- 10.48550/arXiv.math/0603454
- arXiv:
- arXiv:math/0603454
- Bibcode:
- 2006math......3454B
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Representation Theory
- E-Print:
- some references are corrected