Psi-floor diagrams and a Caporaso-Harris type recursion

Details Psi-floor diagrams and a Caporaso-Harris type recursion Psi-floor diagrams and a Caporaso-Harris type recursion

2010-03-10

arxiv.org/abs/1003.2067v2

Mathematics

Algebraic Geometry

minor changes to match the published version

Scientific paper

10.1007/s11856-011-0216-0

Floor diagrams are combinatorial objects which organize the count of tropical plane curves satisfying point conditions. In this paper we introduce Psi-floor diagrams which count tropical curves satisfying not only point conditions but also conditions given by Psi-classes (together with points). We then generalize our definition to relative Psi-floor diagrams and prove a Caporaso-Harris type formula for the corresponding numbers. This formula is shown to coincide with the classical Caporaso-Harris formula for relative plane descendant Gromov-Witten invariants. As a consequence, we can conclude that in our case relative descendant Gromov-Witten invariants equal their tropical counterparts.

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