Dolbeault Cohomology of Complex Manifolds with Torus Action

Student: Krutovskiy Roman

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2020

I describe the basic Dolbealut cohomology algebra of the canonical foliation on a class of complex manifolds with a maximal torus action. I also provide a dga model for the ordinary Dolbeault cohomology algebra. The Hodge decomposition for the basic Dolbeault cohomology is proved by reducing to the transversely Kähler (equivalently, polytopal) case using a foliated analogue of toric blow-up.

Full text (added June 2, 2020)

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