English

The moduli space of tropical curves with fixed Newton polygon

Algebraic Geometry 2025-10-01 v4 Combinatorics

Abstract

Given a lattice polygon, we study the moduli space of all tropical plane curves with that Newton polygon. We determine a formula for the dimension of this space in terms of combinatorial properties of that polygon. We prove that if this polygon is nonhyperelliptic or maximal and hyperelliptic, then this formula matches the dimension of the moduli space of nondegenerate algebraic curves with that given Newton polygon.

Keywords

Cite

@article{arxiv.2002.10874,
  title  = {The moduli space of tropical curves with fixed Newton polygon},
  author = {Desmond Coles and Neelav Dutta and Sifan Jiang and Ralph Morrison and Andrew Scharf},
  journal= {arXiv preprint arXiv:2002.10874},
  year   = {2025}
}

Comments

21 pages, 16 figures