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Symplectic form on hyperpolygon spaces

Indranil Biswas, Carlos Florentino, Leonor Godinho, Alessia Mandini

Abstract

In [GM], a family of parabolic Higgs bundles on $CP^1$ has been constructed and identified with a moduli space of hyperpolygons. Our aim here is to give a canonical alternative construction of this family. This enables us to compute the Higgs symplectic form for this family and show that the isomorphism of [GM] is a symplectomorphism.

Symplectic form on hyperpolygon spaces

Abstract

In [GM], a family of parabolic Higgs bundles on has been constructed and identified with a moduli space of hyperpolygons. Our aim here is to give a canonical alternative construction of this family. This enables us to compute the Higgs symplectic form for this family and show that the isomorphism of [GM] is a symplectomorphism.

Paper Structure

This paper contains 5 sections, 3 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. A family of parabolic Higgs bundles on ${\mathbb C}{\mathbb P}^1$
  3. Symplectic structure on the moduli of parabolic Higgs bundles
  4. A natural $1$--form
  5. The pullback of $\lambda$

Key Result

Proposition \oldthetheorem

The morphism $\varphi$ in e6 is $G$-invariant, inducing the isomorphism constructed in GM.

Theorems & Definitions (4)

  • Proposition \oldthetheorem
  • Theorem \oldthetheorem
  • proof
  • Corollary \oldthetheorem