Stability conditions on a non-compact Calabi-Yau threefold

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 $\PP^2$. 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 $\PP^2$. We give some evidence from mirror symmetry for this conjecture.

A surprising number of errors have been corrected. This is the final version to be published in Communications in Mathematical Physics

References in corpus (1)

• Stability conditions on triangulated categories

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