Intersection of two quadrics: modular interpretation and Hitchin morphism

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Benedetti, Vladimiro, Höring, Andreas, Liu, Jie
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866912415001608192
author Benedetti, Vladimiro
Höring, Andreas
Liu, Jie
author_facet Benedetti, Vladimiro
Höring, Andreas
Liu, Jie
contents The cotangent bundle $T^*X$ of a smooth intersection $X$ of two quadrics admits a Lagrangian fibration determined by the intrinsic geometry of $X$. We show that this fibration is actually the Hitchin morphism if we endow $X$ with a structure of moduli space of twisted Spin-bundles. This generalises the classical result for threefolds, in which case it recovers the Hitchin fibration for the moduli space of rank two bundles with fixed determinant of odd degree on a curve of genus two.
format Preprint
id arxiv_https___arxiv_org_abs_2506_04707
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Intersection of two quadrics: modular interpretation and Hitchin morphism
Benedetti, Vladimiro
Höring, Andreas
Liu, Jie
Algebraic Geometry
14H60, 14D20, 14J45, 14M10
The cotangent bundle $T^*X$ of a smooth intersection $X$ of two quadrics admits a Lagrangian fibration determined by the intrinsic geometry of $X$. We show that this fibration is actually the Hitchin morphism if we endow $X$ with a structure of moduli space of twisted Spin-bundles. This generalises the classical result for threefolds, in which case it recovers the Hitchin fibration for the moduli space of rank two bundles with fixed determinant of odd degree on a curve of genus two.
title Intersection of two quadrics: modular interpretation and Hitchin morphism
topic Algebraic Geometry
14H60, 14D20, 14J45, 14M10
url https://arxiv.org/abs/2506.04707