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Stability Conditions, Wall-crossing and weighted Gromov-Witten Invariants

Arend Bayer·Yuri I. Manin
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Abstract

We extend B. Hassett's theory of weighted stable pointed curves ([Has03]) to weighted stable maps. The space of stability conditions is described explicitly, and the wall-crossing phenomenon studied. This can be considered as a non-linear analog of the theory of stability conditions in abelian and triangulated categories. We introduce virtual fundamental classes and thus obtain weighted Gromov-Witten invariants. We show that by including gravitational descendants, one obtains an $\LL$-algebra as introduced in [LM04] as a generalization of a cohomological field theory.

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Arend Bayer, Yuri I. Manin. 2009-01-20. Stability Conditions, Wall-crossing and weighted Gromov-Witten Invariants. https://arxiv.org/abs/math/0607580

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