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arXiv · 1003.2067

Psi-floor diagrams and a Caporaso-Harris type recursion

Florian Block·Andreas Gathmann·Hannah Markwig
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Abstract

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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Florian Block, Andreas Gathmann, Hannah Markwig. 2010-03-10. Psi-floor diagrams and a Caporaso-Harris type recursion. https://doi.org/10.1007/s11856-011-0216-0

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