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K-stability of Fano 3-folds of Picard rank 3 and degree 22

Ivan Cheltsov

Abstract

We prove K-stability of smooth Fano 3-folds of Picard rank 3 and degree 22 that satisfy very explicit generality condition.

K-stability of Fano 3-folds of Picard rank 3 and degree 22

Abstract

We prove K-stability of smooth Fano 3-folds of Picard rank 3 and degree 22 that satisfy very explicit generality condition.
Paper Structure (7 sections, 28 theorems, 157 equations)

This paper contains 7 sections, 28 theorems, 157 equations.

Table of Contents

  1. Introduction
  2. The proof
  3. $\delta$-invariants of some polarized del Pezzo surfaces
  4. Smooth quintic del Pezzo surface
  5. Quintic del Pezzo surface with singular point of type $\mathbb{A}_1$
  6. Quintic del Pezzo surface with singular point of type $\mathbb{A}_2$
  7. Smooth sextic del Pezzo surface

Key Result

Lemma 1.1

If $L=\{x_0-x_2=0,x_1-x_3=0\}$, then $X$ is K-stable.

Theorems & Definitions (48)

  • Lemma 1.1: Book
  • Theorem 1
  • Corollary 1.1
  • Remark 1
  • Lemma 2.1: cf. CheltsovFujitaKishimotoOkada
  • proof
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • ...and 38 more