Corpus ID: 220525468

Hodge theory for tropical varieties

@article{Amini2020HodgeTF,
  title={Hodge theory for tropical varieties},
  author={O. Amini and Matthieu Piquerez},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}

O. Amini, Matthieu Piquerez

Published 2020

Mathematics

arXiv: Algebraic Geometry

In this paper we prove that the cohomology of smooth projective tropical varieties verify the tropical analogs of three fundamental theorems which govern the cohomology of complex projective varieties: Hard Lefschetz theorem, Hodge-Riemann relations and monodromy-weight conjecture. On the way to establish these results, we introduce and prove other results of independent interest. This includes a generalization of the results of Adiprasito-Huh-Katz, Hodge theory for combinatorial geometries… CONTINUE READING

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