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Tropical moduli spaces of stable maps to a curve. (English) Zbl 1400.14146
Böckle, Gebhard (ed.) et al., Algorithmic and experimental methods in algebra, geometry, and number theory. Cham: Springer (ISBN 978-3-319-70565-1/hbk; 978-3-319-70566-8/ebook). 287-309 (2017).
Summary: We construct moduli spaces of rational covers of an arbitrary smooth tropical curve in \({\mathbb R}^r\) as tropical varieties. They are contained in the balanced fan parametrizing tropical stable maps of the appropriate degree to \({\mathbb R}^r\). The weights of the top-dimensional polyhedra are given in terms of certain lattice indices and local Hurwitz numbers.
For the entire collection see [Zbl 1394.14002].

MSC:
14T05 Tropical geometry (MSC2010)
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
51M20 Polyhedra and polytopes; regular figures, division of spaces
Software:
a-tint; GAP; polymake
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References:
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