Some quadratic inequalities on product varieties

Abstract

We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for semi-stable objects on product varieties. The leading quadratic inequality can be viewed as a weak version of Bogomolov's inequality holding in arbitrary characteristics.

15 pages, all comments are welcome!

References in corpus (4)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Stability conditions on Kuznetsov components
• Stability conditions on product threefolds of projective spaces and Abelian varieties
• Stability conditions on product varieties