2023/06/15 by Tsutsui, Yuki
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.08905
We use ideas from the Strominger--Yau--Zaslow conjecture and microlocal sheaf theory to define graded modules associated with permissible C∞-divisors on compact tropical manifolds. A C∞-divisor is a generalization of a Lagrangian section on an integral affine manifold. The group of C∞-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.