On stability conditions for the quintic threefold

By Chunyi Li. Inventiones Mathematicae, 2018

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We study the Clifford type inequality for a particular type of curves $$C_{2,2,5}$$C2,2,5, 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 $$\mathbf {P}^4_{\mathbb {C}}$$PC4.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/eedf46d4b245e2bc1f39084778f208d7cdc75ce1