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Book Chapter

Tropical eigenwave and intermediate Jacobians

MPS-Authors
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Mikhalkin,  Grigory
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons236516

Zharkov,  Ilia
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1007/978-3-319-06514-4_7
(Publisher version)

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Fulltext (public)

arXiv:1302.0252.pdf
(Preprint), 541KB

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Citation

Mikhalkin, G., & Zharkov, I. (2014). Tropical eigenwave and intermediate Jacobians. In R. Castano-Bernard, F. Catanese, M. Kontsevich, T. Pantev, Y. Soibelman, & I. Zharkov (Eds.), Homological mirror symmetry and tropical geometry (pp. 309-349). Cham: Springer.


Cite as: https://hdl.handle.net/21.11116/0000-0009-E692-E
Abstract
Tropical manifolds are polyhedral complexes enhanced with certain kind of
affine structure. This structure manifests itself through a particular
cohomology class which we call the eigenwave of a tropical manifold. Other wave
classes of similar type are responsible for deformations of the tropical
structure.
If a tropical manifold is approximable by a 1-parametric family of complex
manifolds then the eigenwave records the monodromy of the family around the
tropical limit. With the help of tropical homology and the eigenwave we define
tropical intermediate Jacobians which can be viewed as tropical analogs of
classical intermediate Jacobians.