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 $(\Gamma, D)$ consisting of a st...

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Vydáno v:Journal of the European Mathematical Society : JEMS Ročník 23; číslo 1; s. 185 - 217
Hlavní autoři: Möller, Martin, Ulirsch, Martin, Werner, Annette
Médium: Journal Article
Jazyk:angličtina
Vydáno: Zuerich, Switzerland European Mathematical Society Publishing House 01.01.2021
Témata:
Algebraic geometry
Several complex variables and analytic spaces
moduli spaces
Hodge bundle
canonical divisors
Berkovich spaces
abelian differentials
Tropical geometry
flat surfaces
ISSN:1435-9855, 1435-9863
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Shrnutí: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 $(\Gamma, D)$ consisting of a stable tropical curve $\Gamma$ and a divisor $D$ in the canonical linear system on $\Gamma$, we give a purely combinatorial condition to decide whether there is a smooth curve $X$ over a non-Archimedean field whose stable reduction has $\Gamma$ as its dual tropical curve together with an effective canonical divisor $K_X$ that specializes to $D$.
ISSN:1435-9855
1435-9863
DOI:10.4171/JEMS/1009