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Floor decompositions of tropical curves : the planar case

Brugallé, Erwan
Published in Proceedings of the Gökova Geometry-Topology Conference 2008. Gökova - 2008 - Gökova: Gökova Geometry/Topology Conference (CGT). 2008, p. 64-90
Abstract In a previous paper, we announced a formula to compute Gromov-Witten and Welschinger invariants of some toric varieties, in terms of combinatorial objects called floor diagrams. We give here detailed proofs in the tropical geometry framework, in the case when the ambient variety is a complex surface, and give some examples of computations using floor diagrams. The focusing on dimension 2 is motivated by the special combinatoric of floor diagrams compared to arbitrary dimension. We treat a general toric surface case in this dimension: the curve is given by an arbitrary lattice polygon and include computation of Welschinger invariants with pairs of conjugate points. See also cite{FM} for combinatorial treatment of floor diagrams in the projective case.
Note 20 pages, 17 figures
Stable URL https://archive-ouverte.unige.ch/unige:10796
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ISBN: 978-1-57146-136-0
arXiv: 0812.3354

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Deposited on : 2010-08-23

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