English

Maximal Mumford Curves from Planar Graphs

Algebraic Geometry 2025-04-03 v1 Combinatorics

Abstract

A curve of genus g is maximal Mumford (MM) if it has g+1 ovals and g tropical cycles. We construct full-dimensional families of MM curves in the Hilbert scheme of canonical curves. This rests on first-order deformations of graph curves whose graph is planar.

Keywords

Cite

@article{arxiv.2404.11838,
  title  = {Maximal Mumford Curves from Planar Graphs},
  author = {Mario Kummer and Bernd Sturmfels and Raluca Vlad},
  journal= {arXiv preprint arXiv:2404.11838},
  year   = {2025}
}

Comments

22 pages

R2 v1 2026-06-28T15:58:05.204Z