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Stability Conditions on a Non-Compact Calabi-Yau Threefold

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Abstract

We study the space of stability conditions Stab(X) on the non-compact Calabi-Yau threefold X which is the total space of the canonical bundle of \(\mathbb{P}^2\). We give a combinatorial description of an open subset of Stab(X) and state a conjecture relating Stab(X) to the Frobenius manifold obtained from the quantum cohomology of \(\mathbb{P}^2\). We give some evidence from mirror symmetry for this conjecture.

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  1. School of Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK

    Tom Bridgeland

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  1. Tom Bridgeland
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Communicated by M.R. Douglas

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Bridgeland, T. Stability Conditions on a Non-Compact Calabi-Yau Threefold. Commun. Math. Phys. 266, 715–733 (2006). https://doi.org/10.1007/s00220-006-0048-7

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