Donagi-Markman cubic for Hitchin systems

Donagi-Markman cubic for the generalised Hitchin system

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.

$A_2$、$B_2$、$G_2$ 型 Hitchin 系统的 Donagi-Markman 三次型

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

本文通过计算 Balduzzi-Pantev 公式中的二次留数，获得了 $A_2$、$B_2$ 和 $G_2$ 型 Hitchin 系统的 Donagi-Markman 三次型显式公式，并恢复了 $G_2$ 的早先结果。

Spaces of abelian differentials and Hitchin's spectral covers

Using the embedding of the moduli space of generalized GL(n) Hitchin's spectral covers to the moduli space of meromorphic abelian differentials we study the variational formulae of the period matrix, the canonical bidifferential, the prime form and the Bergman tau function. This leads to residue formulae which generalize the Donagi-Markman formula for variations of the period matrix. Computation of second derivatives of the period matrix reproduces the formula derived by Baraglia and Zhenxi Huang using the framework of topological recursion.

A hyper-Kähler compactification of the Intermediate Jacobian fibration associated to a cubic fourfold

For a general cubic fourfold, it was observed by Donagi and Markman that the relative intermediate Jacobian fibration associated to the family of its hyperplane sections carries a natural holomorphic symplectic form making the fibration Lagrangian. In this paper, we obtain a smooth projective compactification of the intermediate Jacobian fibration giving a ten-dimensional compact hyper-Kähler manifold, which we then show to be deformation equivalent to the exceptional example of O'Grady. This proves a conjecture by Markushevich.

与Fano三维簇相关的Abel-Jacobi映射的Lagrangian解释

Lagrangian interpretation of Abel-Jacobi mappings associated to Fano threefolds

本文利用Donagi-Markman和Markushevich框架，推导Fano三维簇上Abel-Jacobi映射的微分表达式，并用于给出经典结果的新证明。