Derived categories and the genus of space curves

Abstract

We generalize a classical result about the genus of curves in projective space by Gruson and Peskine to principally polarized abelian threefolds of Picard rank one. The proof is based on wall-crossing techniques for ideal sheaves of curves in the derived category. In the process, we obtain bounds for Chern characters of other stable objects such as rank two sheaves. The argument gives a proof for projective space as well. In this case these techniques also indicate an approach for a conjecture by Hartshorne and Hirschowitz and we prove first steps towards it.

41 pages, Second version: Minor changes

References in corpus (4)

• Stability conditions on product threefolds of projective spaces and Abelian varieties
• Bridgeland Stability on Blow Ups and Counterexamples
• The genus of projective curves on complete intersection surfaces
• Hilbert scheme of twisted cubics as simple wall-crossing

Cited by in corpus (6)

• The desingularization of the theta divisor of a cubic threefold as a moduli space
• Walls and asymptotics for Bridgeland stability conditions on 3-folds
• Stability and Applications
• Geometry of canonical genus four curves
• Initial ideals of weighted forms and the genus of locally Cohen-Macaulay curves
• Tilt stability and the degree of irrationality of surfaces on threefolds