Floor decompositions of tropical curves : the planar case
By Erwan Brugallé, G. Mikhalkin. 2008
87 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/33c972d8431a885e4d169c2a0d9e3eebf99a962a
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In Algebra and Number Theory
- Erwan Brugallé
- I. Itenberg
- Kristin M. Shaw
- Filippo Viviani
- Silvia Brannetti
- Margarida Melo
- G. Mikhalkin
- Eugenii Shustin
In Computational Theory and Mathematics
- Erwan Brugallé
- I. Itenberg
- Kristin M. Shaw
- Filippo Viviani
- Melody Chan
- Silvia Brannetti
- Margarida Melo
- G. Mikhalkin
In Geometry and Topology
- Erwan Brugallé
- I. Itenberg
- G. Mikhalkin
- Kristin M. Shaw
- Filippo Viviani
- Silvia Brannetti
- Margarida Melo
- Lucia Caporaso
Citations in the corpus
- Brief introduction to tropical geometry (2015, background): “Tropical formulation of patchworking became natural with the introduction of amoebas due to I.M. Gelfand, M.M. Kapranov and A.V. Zelevinsky [GKZ94], further relations between amoebas and real algebraic curves were found by O. Viro and G. Mikhalkin (see [Vir01] and [Mik00]).”
- Floor diagrams relative to a conic, and GW-W invariants of Del Pezzo surfaces (2014, methodology): “Note that there are slight differences with the original definition of floor diagrams in [BM07], [BM08], and [BM].”
- On the tropical Torelli map (2009, background): “For instance, this program has been carried out successfully for many problems of real and complex enumerative geometry, see for example [32,40,50,24,25,11,33,7,21].”