Tropical curves and covers and their moduli spaces. (English) Zbl 1466.14067
Summary: Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and covers of tropical curves maps between metric graphs satisfying certain conditions. In this short survey, we offer an introduction to the combinatorial theory of abstract tropical curves and covers of curves, and their moduli spaces, and we showcase three results demonstrating how this theory can be applied in algebraic geometry.
MSC:
| 14T20 | Geometric aspects of tropical varieties |
| 14H10 | Families, moduli of curves (algebraic) |
| 14N10 | Enumerative problems (combinatorial problems) in algebraic geometry |
Keywords:
tropical geometry; moduli spaces; tropical covers; mirror symmetry; Hurwitz numbers; enumerative geometrySoftware:
ellipticcovers.libReferences:
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