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Poisson manifolds of strong compact type over 2-tori

Luka Zwaan

Abstract

In arXiv1312.7267, the first non-trivial example of a Poisson manifold of strong compact type is given. The construction uses the theory of K3 surfaces and results in a Poisson manifold with leaf space $S^1$. We modify the construction to obtain a new class of examples. Specifically, we obtain for each strongly integral affine 2-torus a Poisson manifold of strong compact type with said torus as leaf space.

Poisson manifolds of strong compact type over 2-tori

Abstract

In arXiv1312.7267, the first non-trivial example of a Poisson manifold of strong compact type is given. The construction uses the theory of K3 surfaces and results in a Poisson manifold with leaf space . We modify the construction to obtain a new class of examples. Specifically, we obtain for each strongly integral affine 2-torus a Poisson manifold of strong compact type with said torus as leaf space.

Paper Structure

This paper contains 14 sections, 69 equations.

Table of Contents

  1. Introduction
  2. Background & general construction of PMSCTs
  3. The integral affine structure on the leaf space
  4. The linear variation theorem
  5. The construction
  6. Background on K3 surfaces and the Poisson structure on the universal family
  7. The Torelli theorem
  8. Moduli spaces and universal families
  9. The Poisson structure
  10. The action
  11. The examples
  12. The PMSCTs with leaf space the circle
  13. The PMSCTs with leaf space a torus of type (\ref{['torusI']})
  14. The PMSCTs with leaf space a torus of type (\ref{['torusII']})

Theorems & Definitions (7)

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