# Publications

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## Floor decomposition of tropical curves : the planar case

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.