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$\del\delbar$-Lemma and Bott-Chern cohomology of twistor spaces

Anna Fino, Gueo Grantcharov, Nicoletta Tardini, Adriano Tomassini, Luigi Vezzoni

Abstract

In the paper we study the Bott-Chern and Aeppli cohomologies of the twistor space of a compact self-dual 4-manifold and we characterize the validity of the $\partial \overline \partial$-lemma. We also compute explicitly the Dolbeault cohomology of the twistor space $Z$ of the flat $4$-dimensional torus, which is known to not satisfy the $\partial\overline{\partial}$ lemma.

$\del\delbar$-Lemma and Bott-Chern cohomology of twistor spaces

Abstract

In the paper we study the Bott-Chern and Aeppli cohomologies of the twistor space of a compact self-dual 4-manifold and we characterize the validity of the -lemma. We also compute explicitly the Dolbeault cohomology of the twistor space of the flat -dimensional torus, which is known to not satisfy the lemma.

Paper Structure

This paper contains 6 sections, 12 theorems, 54 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Bott-Chern cohomology and $\partial\overline\partial$-lemma
  4. Twistor spaces
  5. Bott-Chern and Aeppli cohomologies of twistor spaces and $\partial\overline\partial$-lemma
  6. Dolbeault cohomology of the twistor space of the torus

Key Result

Theorem 1

Let $X$ be a compact complex manifold. Then, Moreover, the following facts are equivalent:

Theorems & Definitions (22)

  • Theorem 1: angella-tomassiniangella-tardini
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Theorem 5
  • Corollary 6
  • proof
  • ...and 12 more