Realizability of tropical canonical divisors
- We use recent results by Bainbridge–Chen–Gendron–Grushevsky–Möller 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 an effective canonical divisor KX that specializes to D.
