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arXiv · 1103.3995

The Calabi-Yau equation on 4-manifolds over 2-tori

Anna Fino·YanYan Li·Simon Salamon·Luigi Vezzoni
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Abstract

This paper pursues the study of the Calabi-Yau equation on certain symplectic non-Kaehler 4-manifolds, building on a key example of Tosatti-Weinkove in which more general theory had proved less effective. Symplectic 4-manifolds admitting a 2-torus fibration over a 2-torus base are modelled on one of three solvable Lie groups. Having assigned an invariant almost-Kaehler structure and a volume form that effectively varies only on the base, one seeks a symplectic form with this volume. Our approach simplifies the previous analysis of the problem, and establishes the existence of solutions in various other cases.

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Anna Fino, YanYan Li, Simon Salamon, Luigi Vezzoni. 2011-03-21. The Calabi-Yau equation on 4-manifolds over 2-tori. https://arxiv.org/abs/1103.3995

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