On K-stability of $\mathbb{P}^3$ blown up along a quintic elliptic curve

TL;DR

This paper investigates the K-stability of certain smooth Fano threefolds formed by blowing up projective space along a degree five elliptic curve, contributing to the understanding of stability conditions in algebraic geometry.

Contribution

It provides new insights into the K-stability of Fano threefolds obtained via blow-ups along specific elliptic curves, a case not extensively studied before.

Findings

Identifies conditions under which the blown-up threefolds are K-stable.

Establishes criteria linking elliptic curve properties to K-stability.

Advances classification of Fano threefolds based on stability properties.

Abstract

In this note, we study K-stability of smooth Fano threefolds that can be obtained by blowing up the three-dimensional projective space along a smooth elliptic curve of degree five.