Algebraic and tropical curves: comparing their moduli spaces

Details Algebraic and tropical curves: comparing their moduli spaces Algebraic and tropical curves: comparing their moduli spaces

2011-01-25

arxiv.org/abs/1101.4821v3

Mathematics

Algebraic Geometry

Changes in numbering to match the published version

Scientific paper

We construct the moduli space for equivalence classes of n-pointed tropical curves of genus g, together with its compactification given by weighted tropical curves, and establish some of its basic topological properties. We compare it to the moduli spaces of smooth and stable algebraic curves, from the combinatorial, the topological, and the Teichm\"uller point of view. The paper is written in an expository style, and it generalizes some results contained in sections 4-6 of arXiv:1001.2815v3.

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