Moduli space of symplectic log Calabi-Yau divisors and torus fibrations

Abstract: Symplectic log Calabi-Yau divisors are the symplectic analogue of anti-canonical divisors in algebraic geometry. We study the rigidity of such divisors. In particular we prove a Torelli type theorem and form an equivalent moduli space of homology configurations which is more suitable for counting. We also discuss their relations to toric actions and almost toric fibrations, reprove a finiteness result and an upper bound for toric actions by Karshon-Kessler-Pinsonnault, and prove a new stability result.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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