On K-stability of one-nodal prime Fano threefolds of genus $12$

TL;DR

This paper proves that most one-nodal prime Fano threefolds of genus 12 are K-polystable, contributing to the understanding of their geometric stability properties.

Contribution

It establishes K-polystability for general one-nodal prime Fano threefolds of genus 12, a new result in the classification of Fano varieties.

Findings

General one-nodal prime Fano threefolds of genus 12 are K-polystable.

Supports the link between geometric properties and stability in Fano threefolds.

Advances the classification of stable Fano varieties.

Abstract

We show that general one-nodal prime Fano threefolds of genus $12$ are K-polystable.