Type one generalized Calabi--Yaus
| Autor: | Bailey, Michael, Cavalcanti, Gil R R., Gualtieri, Marco, Sub Fundamental Mathematics, Fundamental mathematics |
|---|---|
| Přispěvatelé: | Sub Fundamental Mathematics, Fundamental mathematics |
| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics 53D18 53D17 Symplectic fibration General Physics and Astronomy Physics and Astronomy(all) 01 natural sciences symbols.namesake Mathematics::Algebraic Geometry Euler characteristic 0103 physical sciences FOS: Mathematics Generalized Calabi–Yau 0101 mathematics Mathematics::Symplectic Geometry Mathematical Physics Geometry and topology Mathematics 010102 general mathematics Fibration Cohomology Algebra Differential Geometry (math.DG) Generalized complex structure Generalized complex structures symbols 010307 mathematical physics Geometry and Topology Mathematics::Differential Geometry Complex manifold Signature (topology) Symplectic geometry |
| Zdroj: | Journal of Geometry and Physics, 120, 89. Elsevier |
| ISSN: | 0393-0440 |
| DOI: | 10.48550/arxiv.1611.04319 |
| Popis: | We study type one generalized complex and generalized Calabi--Yau manifolds. We introduce a cohomology class that obstructs the existence of a globally defined, closed 2-form which agrees with the symplectic form on the leaves of the generalized complex structure, the twisting class. We prove that in a compact, type one, 4n-dimensional generalized complex manifold the Euler characteristic must be even and equal to the signature modulo four. The generalized Calabi--Yau condition places much stronger constrains: a compact type one generalized Calabi--Yau fibers over the 2-torus and if the structure has one compact leaf, then this fibration can be chosen to be the fibration by the symplectic leaves of the generalized complex structure. If the twisting class vanishes, one can always deform the structure so that it has a compact leaf. Finally we prove that every symplectic fibration over the 2-torus admits a type one generalized Calabi--Yau structure. Comment: 9 pages |
| Databáze: | OpenAIRE |
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