On stability conditions for the quintic threefold

2018/10/31 by Chunyi Li · 1 citation
Mathematics · #math.AG #msc:14F05 #msc:14J32 #msc:18E30

paper · pdf · doi:10.1007/s00222-019-00888-z

pre-journal version, 32 pages, 7 figures, comments are very welcome!

arxiv created 2019/04/29 · arxiv updated 2019/10/02

Abstract

We study the Clifford type inequality for a particular type of curves C_2,2,5, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previous framework by Bayer, Bertram, Macrì, Stellari and Toda, we construct an open subset of stability conditions on every smooth quintic threefold in P⁴_{\mathbb C}.

Cited by

• Bogomolov type inequalities and Frobenius semipositivity