Stability conditions on Calabi-Yau double/triple solids

TL;DR

This paper establishes a stronger Bogomolov-Gieseker inequality for stable sheaves on specific Calabi-Yau threefolds and uses it to construct Bridgeland stability conditions, advancing understanding of stability in algebraic geometry.

Contribution

It proves a stronger BG inequality for certain Calabi-Yau threefolds and constructs new Bridgeland stability conditions using this inequality.

Findings

Proved a stronger BG inequality for weighted hypersurfaces in specific projective spaces.

Constructed open subsets of Bridgeland stability conditions on these Calabi-Yau threefolds.

Enhanced the theoretical framework for stability conditions in algebraic geometry.

Abstract

In this paper, we prove a stronger form of the Bogomolov-Gieseker (BG) inequality for stable sheaves on two classes of Calabi-Yau threefolds, namely, weighted hypersurfaces inside the weighted projective spaces $\mathbb{P}(1, 1, 1, 1, 2)$ and $\mathbb{P}(1, 1, 1, 1, 4)$. Using the stronger BG inequality as a main technical tool, we construct open subsets in the spaces of Bridgeland stability conditions on these Calabi-Yau threefolds.