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A support theorem for the Hitchin fibration: the case of $\text{SL}_{n}$

Part of: Curves Families, fibrations

Published online by Cambridge University Press:  26 April 2017

Mark Andrea de Cataldo
Mark Andrea de Cataldo*
Affiliation:
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651, USA email [email protected]
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Abstract

We prove that the direct image complex for the $D$-twisted $\text{SL}_{n}$ Hitchin fibration is determined by its restriction to the elliptic locus, where the spectral curves are integral. The analogous result for $\text{GL}_{n}$ is due to Chaudouard and Laumon. Along the way, we prove that the Tate module of the relative Prym group scheme is polarizable, and we also prove $\unicode[STIX]{x1D6FF}$-regularity results for some auxiliary weak abelian fibrations.

Keywords

Hitchin morphismspecial linear groupdecomposition theoremsupports

MSC classification

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles 14H60: Vector bundles on curves and their moduli
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 6 , June 2017 , pp. 1316 - 1347
Copyright
© The Author 2017 

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