On K-stability for Fano threefolds of rank 3 and degree 28

TL;DR

This paper demonstrates the existence of a specific class of smooth Fano threefolds with certain stability, degree, and topological properties, expanding the understanding of K-stability in algebraic geometry.

Contribution

It establishes the existence of a K-stable smooth Fano threefold with Picard rank 3, anti-canonical degree 28, and third Betti number 2, a previously unknown example.

Findings

Existence of a K-stable smooth Fano threefold with specified properties

Provides new example in the classification of Fano threefolds

Advances understanding of K-stability conditions

Abstract

We show that there exists a K-stable smooth Fano threefold of the Picard rank 3, the anti-canonical degree 28 and the third Betti number 2.