Session S35 - Moduli Spaces in Algebraic Geometry and Applications

Thursday, July 15, 14:00 ~ 14:40 UTC-3

Geometric stability conditions under autoequivalences

Cristian Martinez

Universidade Estadual de Campinas , Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

There is a natural action of the group of autoequivalences of the derived category of a variety on its stability manifold. On a surface, most of the applications of the theory of Bridgeland stability conditions to the study of the geometry of moduli spaces of Gieseker semistable sheaves come from the study of the wall-crossing phenomena for families of geometric stability conditions (stability conditions for which all the skyscraper sheaves are stable). However, it is not always easy to identify nontrivial autoequivalences (other than shifting, and tensoring by line bundles), and even if we do, it is not always the case that the image of a geometric stability condition by such autoequivalence is again geometric. When this happens, we get a valuable tool to get results about the non-emptiness, projectivity, and even irreducibility of some Bridgeland moduli spaces. In this talk, I will present some instances where stability is preserved by a nontrivial autoequivalence, including elliptic and blow-up surfaces.

Joint work with Jason Lo (California State University, Northridge, USA).

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