Algebraic and tropical curves: comparing their moduli spaces
By Lucia Caporaso. 2011
89 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1e071f6d6ee7f7b63190234ab3efb034540d183a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Computational Theory and Mathematics
- Dhruv Ranganathan
- Renzo Cavalieri
- Melody Chan
- Hannah Markwig
- Martin Ulirsch
- Lucia Caporaso
- G. Mikhalkin
In Geometry and Topology
- Dhruv Ranganathan
- Renzo Cavalieri
- Melody Chan
- Hannah Markwig
- Martin Ulirsch
- Lucia Caporaso
- G. Mikhalkin
Citations in the corpus
- Tropical hyperelliptic curves (2011, background): “Our work ties together two strands in the recent tropical geometry literature: tropical Brill-Noether theory on the one hand [Bak08], [Cap11b], [CDPR10], [LPP11]; and tropical moduli spaces of curves on the other [BMV11], [Cap10], [Cap11a], [Cha11], [MZ07].”
- Tropicalizing the space of admissible covers (2014, background): “The moduli space of genus g tropical curves, roughly speaking, parametrizes vertex weighted metric graphs of a given genus [8, 10, 13].”