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On Fourier-Mukai type autoequivalences of Kuznetsov components of cubic threefolds

Ziqi Liu

Abstract

We determine the group of all Fourier-Mukai type autoequivalences of Kuznetsov components of smooth complex cubic threefolds, and provide yet another proof for the Fourier-Mukai version of categorical Torelli theorem for smooth complex cubic threefolds.

On Fourier-Mukai type autoequivalences of Kuznetsov components of cubic threefolds

Abstract

We determine the group of all Fourier-Mukai type autoequivalences of Kuznetsov components of smooth complex cubic threefolds, and provide yet another proof for the Fourier-Mukai version of categorical Torelli theorem for smooth complex cubic threefolds.
Paper Structure (7 sections, 26 theorems, 49 equations)

This paper contains 7 sections, 26 theorems, 49 equations.

Table of Contents

  1. Introduction
  2. Organization
  3. Conventions
  4. Kuznetsov components of cubic threefolds
  5. Fourier--Mukai transforms
  6. The group of Fourier--Mukai type autoequivalences
  7. The Fourier--Mukai type categorical Torelli theorem revisited

Key Result

Theorem 1.1

One has $\mathop{\mathrm{Aut}}\nolimits_{FM}(\mathcal{A}_Y)\cong\mathbb{Z}\times\mathop{\mathrm{Aut}}\nolimits(Y)$.

Theorems & Definitions (52)

  • Theorem 1.1: Theorem \ref{['5_main-theorem']}
  • Theorem 1.2: Theorem \ref{['5_another-proof']}
  • Example 2.1
  • Example 2.2
  • Example 2.3
  • Example 2.4
  • Example 2.5
  • Proposition 2.6: BMMS12
  • Example 2.7
  • Proposition 2.8
  • ...and 42 more