2017/10/17 by Moeller, Martin, Ulirsch, Martin, Werner, Annette · 1 citation
#14H10 #14H51 #14T05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1710.06401
We use recent results by Bainbridge-Chen-Gendron-Grushevsky-Moeller on compactifications of strata of abelian differentials to give a comprehensive solution to the realizability problem for effective tropical canonical divisors in equicharacteristic zero. Given a pair (Γ, D) consisting of a stable tropical curve Γ and a divisor D in the canonical linear system on Γ, we give a purely combinatorial condition to decide whether there is a smooth curve X over a non-Archimedean field whose stable reduction has Γ as its dual tropical curve together with a effective canonical divisor KX that specializes to D. Along the way, we develop a moduli-theoretic framework to understand Baker's specialization of divisors from algebraic to tropical curves as a natural toroidal tropicalization map in the sense of Abramovich-Caporaso-Payne.