Maximal Mumford Curves from Planar Graphs

Published 18 Apr 2024 in math.AG and math.CO | (2404.11838v1)

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.

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