Stability conditions on a non-compact Calabi-Yau threefold

Details Stability conditions on a non-compact Calabi-Yau threefold Stability conditions on a non-compact Calabi-Yau threefold

2005-09-02

arxiv.org/abs/math/0509048v2

Commun.Math.Phys. 266 (2006) 715-733

Mathematics

Algebraic Geometry

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

Scientific paper

10.1007/s00220-006-0048-7

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.

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