Improved bounds on the number of holomorphic maps between compact Riemann surfaces
Complex Variables
2026-05-21 v1 Algebraic Geometry
Abstract
We give new upper bounds for the number of nonconstant holomorphic maps depending only on the genus. Our estimates improve previously known bounds. The proof is based on the study of pullbacks of holomorphic differentials, together with techniques from the geometry of numbers and the theory of Jacobian varieties.
Cite
@article{arxiv.2605.21137,
title = {Improved bounds on the number of holomorphic maps between compact Riemann surfaces},
author = {Masaharu Tanabe},
journal= {arXiv preprint arXiv:2605.21137},
year = {2026}
}