Counterexample to the Generalized Bogomolov-Gieseker Inequality for Threefolds

TL;DR

This paper presents a counterexample to a conjectured inequality in algebraic geometry, specifically for threefolds, by examining a blow-up of projective space.

Contribution

The authors provide the first known counterexample to the generalized Bogomolov-Gieseker inequality for threefolds, challenging previous conjectures.

Findings

Counterexample constructed using blow-up of a point over three-dimensional projective space

Disproves the conjectured inequality for certain threefolds

Implications for stability conditions in algebraic geometry

Abstract

We give a counterexample to the generalized Bogomolov-Gieseker inequality for threefolds conjectured by Bayer, Macr\`i and Toda using the blow up of a point over three dimensional projective space.