Stability conditions on product varieties

Abstract

Given a stability condition on a smooth projective variety $X$, we construct a family of stability conditions on $X\times C$, where $C$ is a smooth projective curve. In particular, this gives the existence of stability conditions on arbitrary products of curves. The proof uses, by following an idea of Toda, the positivity lemma established by Bayer and Macrì and weak stability conditions on the Abramovich-Polishchuk heart of a bounded t-structure in $D(X\times C)$.

arXiv comment23 pages. v2: addressed referee comments. To appear in Crelle's Journal

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Cited by in corpus (3)

• Some remarks on Fano threefolds of index two and stability conditions
• Stability conditions on Calabi-Yau double/triple solids
• Some quadratic inequalities on product varieties