Computing certain Gromov-Witten invariants of the crepant resolution of P(1,3,4,4)

Samuel Boissière (1) , Etienne Mann (2, 3) , Fabio Perroni (4)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier
3 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
4 Mathematisches Institut [Bayreuth]

We prove a formula computing the Gromov-Witten invariants of genus zero with three marked points of the resolution of the transversal A3 - singularity of the weighted projective space P(1, 3, 4, 4) using the theory of deformations of surfaces with An -singularities. We use this result to check Ruan's conjecture for the stack P(1, 3, 4, 4).

Domaines: Géométrie algébrique [math.AG]

Samuel Boissière, Etienne Mann, Fabio Perroni. Computing certain Gromov-Witten invariants of the crepant resolution of P(1,3,4,4). Nagoya Mathematical Journal, 2011, 201, pp.1-22. ⟨10.1215/00277630-2010-015⟩. ⟨hal-00789790⟩