Algebraic and tropical curves: comparing their moduli spaces

Understand

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.