Balancing properties of tropical moduli maps

Karl Christ; Xiang He; Ilya Tyomkin

doi:10.1112/blms.70297

Balancing properties of tropical moduli maps

Karl Christ
, Xiang He
, Ilya Tyomkin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Given a family of parameterized algebraic curves over a strictly semistable pair, we show that the simultaneous tropicalization of the curves in the family forms a family of parameterized tropical curves over the skeleton of the strictly semistable pair. We show that the induced tropical moduli map satisfies a certain balancing condition, which allows us to describe properties of its image and deduce a new liftability criterion.

Original language	English
Article number	e70297
Journal	Bulletin of the London Mathematical Society
Volume	58
Issue number	2
DOIs	https://doi.org/10.1112/blms.70297
State	Published - 1 Feb 2026

ASJC Scopus subject areas

General Mathematics

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title = "Balancing properties of tropical moduli maps",

abstract = "Given a family of parameterized algebraic curves over a strictly semistable pair, we show that the simultaneous tropicalization of the curves in the family forms a family of parameterized tropical curves over the skeleton of the strictly semistable pair. We show that the induced tropical moduli map satisfies a certain balancing condition, which allows us to describe properties of its image and deduce a new liftability criterion.",

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AU - He, Xiang

AU - Tyomkin, Ilya

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N2 - Given a family of parameterized algebraic curves over a strictly semistable pair, we show that the simultaneous tropicalization of the curves in the family forms a family of parameterized tropical curves over the skeleton of the strictly semistable pair. We show that the induced tropical moduli map satisfies a certain balancing condition, which allows us to describe properties of its image and deduce a new liftability criterion.

AB - Given a family of parameterized algebraic curves over a strictly semistable pair, we show that the simultaneous tropicalization of the curves in the family forms a family of parameterized tropical curves over the skeleton of the strictly semistable pair. We show that the induced tropical moduli map satisfies a certain balancing condition, which allows us to describe properties of its image and deduce a new liftability criterion.

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DO - 10.1112/blms.70297

M3 - Article

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JO - Bulletin of the London Mathematical Society

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Balancing properties of tropical moduli maps

Abstract

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