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K-stability of Fano 3-folds of Picard rank 3 and degree 20

Elena Denisova

Abstract

We prove K-stability of smooth Fano 3-folds of Picard rank 3 and degree 20 that satisfy very explicit generality condition.

K-stability of Fano 3-folds of Picard rank 3 and degree 20

Abstract

We prove K-stability of smooth Fano 3-folds of Picard rank 3 and degree 20 that satisfy very explicit generality condition.
Paper Structure (6 sections, 9 theorems, 111 equations)

This paper contains 6 sections, 9 theorems, 111 equations.

Table of Contents

  1. Introduction
  2. The Proof
  3. Polarized $\delta$-invariant via Kento Fujita’s formulas
  4. Polarized $\delta$-invariant on Del Pezzo surface of degree $4$ with $\mathbb{A}_1$ singularity.
  5. Polarized $\delta$-invariant on Del Pezzo surface of degree $4$ with two $\mathbb{A}_1$ singularities.
  6. Polarized $\delta$-invariant on Del Pezzo surface of degree $4$ with $\mathbb{A}_2$ singularity

Key Result

Theorem 1

If all ramification points of $\eta$ have ramification index two, then $X$ is K-stable.

Theorems & Definitions (16)

  • Example 1
  • Conjecture 1: Book
  • Theorem
  • Conjecture 2
  • Lemma 2.1
  • Lemma 2.2
  • Remark 1
  • Lemma A.1
  • proof
  • Corollary A.1
  • ...and 6 more