Mirror of orbifold singularities in the Hitchin fibration: The case (SLn,PGLn)

IF 1.5 1区 数学 Q1 MATHEMATICS
Yongbin Ruan , Cheng Shu
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引用次数: 0

Abstract

We study the geometry of singular SLn-Hitchin fibres over the elliptic locus. We show that orbifold singularities appear in the PGLn-moduli space MCell(PGLn) exactly when the SLn side MCell(SLn) has a reducible Hitchin fibre. Our main theorem shows that the Fourier-Mukai transform of a skyscraper sheaf supported at an orbifold singularity in MCell(PGLn) satisfies a version of the fractional Hecke eigenproperty, as conjectured by Frenkel and Witten.
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来源期刊
Advances in Mathematics
Advances in Mathematics 数学-数学
CiteScore
2.80
自引率
5.90%
发文量
497
审稿时长
7.5 months
期刊介绍: Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
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