Resumen de Refined floor diagrams from higher genera and lambda classes

Pierrick Bousseau

• We show that, after the change of variables q=eiu, 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 a non-trivial relation between relative and log Gromov–Witten invariants for P2 and Hirzebruch surfaces. We also prove that the Block–Göttsche invariants of F0 and F2 are related by the Abramovich–Bertram formula.