Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces

TL;DR

This paper establishes a Clifford type inequality for a specific Calabi-Yau threefold, leading to a stronger Bogomolov-Gieseker inequality and the construction of Bridgeland stability conditions.

Contribution

It proves a new Clifford type inequality for the intersection of a quartic and quadratics in projective space, enhancing stability condition theory on this Calabi-Yau threefold.

Findings

Proved a Clifford type inequality for $X_{2,2,2,4}$

Derived a stronger Bogomolov-Gieseker inequality for stable bundles

Constructed an open subset of Bridgeland stability conditions

Abstract

In this paper, we prove a Clifford type inequality for the curve $X_{2,2,2,4}$, which is the intersection of a quartic and three general quadratics in $\mathbb{P}^5$. We thus prove a stronger Bogomolov-Gieseker inequality for characters of stable vector bundles and stable objects on $X_{2,4}$. Applying the scheme proposed by Bayer, Bertram, Macr\`i, Stellari and Toda, we can construct an open subset of Bridgeland stability conditions on $X_{2,4}$.