Tropical Homology

By I. Itenberg, L. Katzarkov, G. Mikhalkin, I. Zharkov. 2016

79 citations recorded by the source corpus.

Given a tropical variety X and two non-negative integers p and q we define a homology group $$H_{p,q}(X)$$Hp,q(X) which is a finite-dimensional vector space over $${\mathbb {Q}}$$Q. We show that if X is a smooth tropical variety that can be represented as the tropical limit of a 1-parameter family of complex projective varieties, then $$\dim H_{p,q}(X)$$dimHp,q(X) coincides with the Hodge number $$h^{p,q}$$hp,q of a general member of the family.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b71ce1b2d9f7088f27065af18cb13883d9cc8368

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Erwan Brugallé
2. I. Itenberg
3. Kristin M. Shaw
4. G. Mikhalkin
5. Eugenii Shustin
6. Eric Katz
7. Matthew Baker
8. Melody Chan

In Geometry and Topology

1. Erwan Brugallé
2. I. Itenberg
3. G. Mikhalkin
4. Kristin M. Shaw
5. Eugenii Shustin
6. Viatcheslav Kharlamov
7. Brett Parker
8. O. Y. Viro

In Statistical and Nonlinear Physics

1. G. Mikhalkin
2. Erwan Brugallé

Citations in the corpus

• Brief introduction to tropical geometry (2015, background): “ nite. Then the weight of the ane k-space lim t→+∞ trop M((C×)k) from Example 5.12 coincides with the cardinality of Zk~Im (M). The following theorem generalizes Theorems 2.12 and 5.6. Theorem 5.15 ([IKMZ]). The tropical limit lim t→+∞ trop V t is a tropical subvariety of Rn. Denition 5.16. A tropic”