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
    5 Citations

    Figures from this paper

    A homology theory for tropical cycles on integral affine manifolds and a perfect pairing
    • 4
    • Highly Influenced
    • PDF
    On the tropical Lefschetz-Hopf trace formula
    • PDF

    References

    SHOWING 1-10 OF 113 REFERENCES