A MODULI STACK OF TROPICAL CURVES
A MODULI STACK OF TROPICAL CURVES
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DOI：
10.1017/fms.2020.16
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发表时间：
2020-04-24
影响因子：
1.7
通讯作者：
Wise, Jonathan
中科院分区：
文献类型：
--
作者：
Cavalieri, Renzo;Chan, Melody;Wise, Jonathan
我们致力于制定热带模量问题，并以曲线模空间作为我们的主要例子，为热带几何的基础做出贡献。我们提出了曲线模空间的模函子，并证明它可以通过有理多面锥体类别上的几何堆栈来表示。在这个框架中，具有标记点的曲线模空间之间的自然遗忘态射充当通用曲线。我们的热带几何方法允许热带模数问题（曲线模数或其他）扩展到对数方案。我们用它来构造从代数曲线的模空间到热带曲线的模空间的平滑热带化态射，并且我们证明该态射与所有同义反复态射可交换。
We contribute to the foundations of tropical geometry with a view toward formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose a moduli functor for the moduli space of curves and show that it is representable by a geometric stack over the category of rational polyhedral cones. In this framework, the natural forgetful morphisms between moduli spaces of curves with marked points function as universal curves. Our approach to tropical geometry permits tropical moduli problems-moduli of curves or otherwise-to be extended to logarithmic schemes. We use this to construct a smooth tropicalization morphism from the moduli space of algebraic curves to the moduli space of tropical curves, and we show that this morphism commutes with all of the tautological morphisms.