Abstract |
In [BM07] 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 ofWelschinger invariants with pairs
of conjugate points. See also [FM] for combinatorial treatment of floor diagrams in
the projective case.
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