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

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 sh...

Full description

Saved in:
Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2025-02, Vol.461, p.110076, Article 110076
Main Authors: Ruan, Yongbin, Shu, Cheng
Format: Article
Language:English
Subjects:
Geometric endoscopy
Hitchin fibration
SYZ mirror symmetry
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0001-8708
DOI:10.1016/j.aim.2024.110076