Donagi-Markman cubic for the generalised Hitchin system

TL;DR

This paper extends the understanding of the Donagi-Markman cubic to the G-generalised Hitchin system, proving that the Balduzzi--Pantev formula applies along maximal rank symplectic leaves, enhancing the geometric understanding of integrable systems.

Contribution

It demonstrates that the Balduzzi--Pantev formula for the cubic holds in the context of the G-generalised Hitchin system along maximal rank symplectic leaves.

Findings

The formula applies to the G-generalised Hitchin system.

The cubic is encoded in the third symmetric power of the cotangent bundle.

The result extends previous work on the ordinary Hitchin system.

Abstract

Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We prove that the Balduzzi--Pantev formula holds along maximal rank symplectic leaves of the G-generalised Hitchin system.