@article{66336,
  abstract     = {{<jats:p>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.</jats:p>
	  <jats:p>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.</jats:p>}},
  author       = {{Cavalieri, Renzo and Chan, Melody and Ulirsch, Martin and Wise, Jonathan}},
  issn         = {{2050-5094}},
  journal      = {{Forum of Mathematics, Sigma}},
  publisher    = {{Cambridge University Press (CUP)}},
  title        = {{{A MODULI STACK OF TROPICAL CURVES}}},
  doi          = {{10.1017/fms.2020.16}},
  volume       = {{8}},
  year         = {{2020}},
}