arXiv subjects

Yuki Tsutsui

Publications and source records attributed to Yuki Tsutsui.

2 recordsLinked to original sources

arXiv2024

The complement of tropical curves in moderate position on tropical surfaces

López de Medrano, Rincón and Shaw defined the Chern classes on tropical manifolds as an extension of their theory of the Chern-Schwartz-MacPherson cycles on matroids. This makes it possible to define the Riemann-Roch number of tropical Cartier divisors on compact tropical manifolds. In this paper, we introduce the notion of a moderate position, and discuss a conjecture that the Riemann-Roch number $\operatorname{RR}(X;D)$ of a tropical submanifold $D$ of codimension $1$ in moderate position on a compact tropical manifold $X$ is equal to the topological Euler characteristic of the complement $X\setminus D$. In particular, we prove it and its generalization when $\dim X=2$ and $X$ admits a Delzant face structure.

math.AG↗

arXiv2023

Graded modules associated with permissible $C^{\infty}$-divisors on tropical manifolds

We use ideas from the Strominger--Yau--Zaslow conjecture and microlocal sheaf theory to define graded modules associated with permissible $C^{\infty}$-divisors on compact tropical manifolds. A $C^{\infty}$-divisor is a generalization of a Lagrangian section on an integral affine manifold. The group of $C^{\infty}$-divisors on a tropical manifold surjects onto the Picard group. We also prove a Riemann--Roch formula for compact tropical curves and integral affine manifolds admitting Hessian forms. Our approach differs from the tropical Riemann--Roch theorem established by Gathmann and Kerber.

math.AG↗