English

Tropical intersection homology

Algebraic Geometry 2026-05-14 v4 Number Theory

Abstract

Numerical equivalence of algebraic cycles is defined abstractly by intersection numbers. Classically, for smooth complex proper toric varieties, the quotients by numerical equivalence with rational coefficients can be described geometrically as singular cohomology. They are also expressed in terms of tropical geometry, tropical cohomology, introduced by Itenberg-Katzarkov-Mikhalkin-Zharkov. This paper aims to generalize this to suitable pairs of smooth proper varieties and divisors by introducing a tropical analog of intersection homology.

Keywords

Cite

@article{arxiv.2412.20748,
  title  = {Tropical intersection homology},
  author = {Ryota Mikami},
  journal= {arXiv preprint arXiv:2412.20748},
  year   = {2026}
}

Comments

82 pages. v.2, v.3, v.4:very minor changes