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Abstract: We study the space of stability conditions on the total space of thecanonical bundle over the projective plane. We explicitly describe a chamber ofgeometric stability conditions, and show that its translates viaautoequivalences cover a whole connected component. We prove that thisconnected component is simply-connected. We determine the group ofautoequivalences preserving this connected component, which turns out to beclosely related to Gamma13.Finally, we show that there is a submanifold isomorphic to the universalcovering of a moduli space of elliptic curves with Gamma13-level structure.The morphism is Gamma13-equivariant, and is given by solutions ofPicard-Fuchs equations. This result is motivated by the notion of Pi-stabilityand by mirror symmetry.



Author: Arend Bayer, Emanuele Macri

Source: https://arxiv.org/







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