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Mathematics > Algebraic Geometry

arXiv:1807.10449 (math)
[Submitted on 27 Jul 2018 (v1), last revised 14 Aug 2018 (this version, v2)]

Title:Towards transverse toric geometry

Authors:Hiroaki Ishida
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Abstract: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.
Comments: 46 pages. Remarks 6.5, 6.12, 6.16 and 8.2 added. Typos fixed. References updated. Comments are welcome
Subjects: Algebraic Geometry (math.AG); Algebraic Topology (math.AT); Complex Variables (math.CV); Differential Geometry (math.DG); Symplectic Geometry (math.SG)
MSC classes: 14M25 (Primary) 53C12, 53D20, 57S25, 57R30 (Secondary)
Cite as: arXiv:1807.10449 [math.AG]
  (or arXiv:1807.10449v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.10449

Submission history

From: Hiroaki Ishida [view email]
[v1] Fri, 27 Jul 2018 06:05:44 UTC (39 KB)
[v2] Tue, 14 Aug 2018 08:49:45 UTC (37 KB)
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