2016/04/13 by Paul Alexander Helminck, Helminck, Paul Alexander
Computer Science · Mathematics · Physics and Astronomy · #11G20 #14G22 #14H30 #14T05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1604.03987
openalex publication_date 2016/04/13 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28
Let X be a smooth geometrically connected projective curve of genus two over a complete non-archimedean field K. For discretely valued K, the first main theorem in \citeliu gives a set of criteria on the Igusa invariants of the curve that determine the minimal Berkovich skeleton of X together with its edge lengths and vertex weights. In this paper we use the theory of Berkovich spaces to give a new proof of this theorem that works for arbitrary complete non-archimedean fields. We furthermore interpret the final result in terms of tropical moduli spaces and tropical Igusa invariants. This reformulation shows that the abstract tropicalization map M2\totrop(M2) factors through the tropicalization of a concrete embedding of M2 into a weighted projective space.