Donagi-Markman cubics for Hitchin systems of type A2, B2. G2

TL;DR

This paper derives explicit formulas for the Donagi-Markman cubic in Hitchin systems of types A2, B2, and G2, enhancing understanding of their geometric structures and connecting to previous results for G2.

Contribution

It provides explicit formulas for the Donagi-Markman cubic for specific Hitchin systems, using quadratic residues and previous results, advancing the computational understanding of these systems.

Findings

Explicit formulas for A2, B2, G2 Hitchin systems

Connection to previous G2 results

Method using quadratic residues in Balduzzi-Pantev formula

Abstract

We obtain explicit formulae for the Donagi-Markman (Bryant-Griffiths, Yukawa) cubic for Hitchin systems of type $A_2$, $B_2$ and $G_2$. This is achieved by evaluating the quadratic residues in the Balduzzi-Pantev formula, using a previous result of ours. For $G_2$ we also recover earlier results of Hitchin.