Chern degree functions

Abstract

We introduce Chern degree functions for complexes of coherent sheaves on a polarized surface, which encode information given by stability conditions on the boundary of the $(\alpha ,\beta )$-plane. We prove that these functions extend to continuous real valued functions and we study their differentiability in terms of stability. For abelian surfaces, Chern degree functions coincide with the cohomological rank functions defined by Jiang-Pareschi. We illustrate in some geometrical situations a general strategy to compute these functions.

arXiv commentMinor changes. Final version, to appear in Commun. Contemp. Math

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Cited by in corpus (1)

• Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces