On K-stability of $\mathbb P^3$ blown up along a smooth genus $2$ curve of degree $5$

TL;DR

This paper proves K-stability for infinitely many smooth Fano threefolds obtained by blowing up ^3 along a smooth genus 2 curve of degree 5, contributing to the classification of stable Fano varieties.

Contribution

It establishes K-stability for a new family of Fano threefolds in the Mukai-Mori classification, specifically those blown up along a genus 2 curve of degree 5.

Findings

Proves K-stability for infinitely many such threefolds

Identifies specific geometric conditions ensuring stability

Advances understanding of stability in Fano threefolds

Abstract

We prove K-stability for infinitely many smooth members of the family 2.19 of the Mukai-Mori classification.