Refined floor diagrams from higher genera and lambda classes

2019/04/30 by Pierrick Bousseau · 1 citation
Mathematics · #math.AG

paper · pdf · doi:10.1007/s00029-021-00667-w

44 pages, 8 figures, revised version, exposition greatly improved, main results unchanged, published in Selecta Mathematica

arxiv created 2021/06/05 · arxiv updated 2021/06/08

Abstract

We show that, after the change of variables q=e^iu, refined floor diagrams for ℙ² and Hirzebruch surfaces compute generating series of higher genus relative Gromov-Witten invariants with insertion of a lambda class. The proof uses an inductive application of the degeneration formula in relative Gromov-Witten theory and an explicit result in relative Gromov-Witten theory of ℙ¹. Combining this result with the similar looking refined tropical correspondence theorem for log Gromov-Witten invariants, we obtain some non-trivial relation between relative and log Gromov-Witten invariants for ℙ² and Hirzebruch surfaces. We also prove that the Block-Göttsche invariants of \mathbbF₀ and \mathbbF₂ are related by the Abramovich-Bertram formula.

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