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Towards transverse toric geometry

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arxiv 1807.10449 v2 pith:CHTNL7UK submitted 2018-07-27 math.AG math.ATmath.CVmath.DGmath.SG

Hiroaki Ishida This is my paper · ORCID
classification math.AGmath.ATmath.CVmath.DGmath.SG
keywords themalgebrasbasiccohomologyfansmarkedtoricbehave
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We study certain foliated complex manifolds that behave similarly to complete nonsingular toric varieties. We classify them by combinatorial objects that we call marked fans. We describe the basic cohomology algebras of them in terms of corresponding marked fans. We also study the basic Dolbeault cohomology algebras of them.

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  1. Dolbeault cohomology of complex manifolds with torus action

    math.DG 2019-08 conditional novelty 7.0 of 10

    The basic Dolbeault cohomology of the canonical foliation on complex moment-angle manifolds and manifolds with maximal torus action admits a Hodge decomposition and is generated by degree (1,1) classes.

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