The space of stability conditions on the local projective plane

DOI10.1215/00127094-1444249zbMATH Open1238.14014arXiv0912.0043OpenAlexW3106489028MaRDI QIDQ650996

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Publication date: 8 December 2011

Published in: (Search for Journal in Brave)

Abstract: We study the space of stability conditions on the total space of the canonical bundle over the projective plane. We explicitly describe a chamber of geometric stability conditions, and show that its translates via autoequivalences cover a whole connected component. We prove that this connected component is simply-connected. We determine the group of autoequivalences preserving this connected component, which turns out to be closely related to Gamma1(3). Finally, we show that there is a submanifold isomorphic to the universal covering of a moduli space of elliptic curves with Gamma1(3)-level structure. The morphism is Gamma1(3)-equivariant, and is given by solutions of Picard-Fuchs equations. This result is motivated by the notion of Pi-stability and by mirror symmetry.

Full work available at URL: https://arxiv.org/abs/0912.0043

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