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A note on cohomology mirror symmetry of toric manifolds

Hao Wen

Abstract

In this note we describe a logarithmic version of mirror Landau-Ginzburg model for a semi-projective toric manifold and show the ring of state space of the Landau-Ginzburg model is isomorphic to the $\C$-valued cohomology of the toric manifold.

A note on cohomology mirror symmetry of toric manifolds

Abstract

In this note we describe a logarithmic version of mirror Landau-Ginzburg model for a semi-projective toric manifold and show the ring of state space of the Landau-Ginzburg model is isomorphic to the -valued cohomology of the toric manifold.

Paper Structure

This paper contains 8 sections, 7 theorems, 56 equations.

Table of Contents

  1. Introduction
  2. Spaces associated to the defining fan of a toric manifold
  3. Presheaves and Čech complexes
  4. A differential graded algebra that computes $H^\bullet(X_\Sigma)$
  5. Local model
  6. Čech model
  7. Landau-Ginzburg mirror for semiprojective toric manifolds
  8. Proof of Theorem \ref{['algebraic exact']}

Key Result

Theorem 3.2

The complex (algebraic model) is exact.

Theorems & Definitions (18)

  • Definition 3.1
  • Theorem 3.2
  • Proposition 4.1
  • proof
  • Lemma 5.1
  • proof
  • Remark 5.2
  • Theorem 5.3
  • proof
  • Example 5.4
  • ...and 8 more