The cohomological crepant resolution conjecture for P(1,3,4,4)

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

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

We compare the Chen-Ruan cohomology ring of the weighted projective spaces $\IP(1,3,4,4)$ and $\IP(1,...,1,n)$ with the cohomology ring of their crepant resolutions. In both cases, we prove that the Chen-Ruan cohomology ring is isomorphic to the quantum corrected cohomology ring of the crepant resolution after suitable evaluation of the quantum parameters. For this, we prove a formula for the Gromov-Witten invariants of the resolution of a transversal ${\rm A}_3$ singularity.

Mots clés: Ruan's conjecture; crepant resolution; Gromov-Witten invariants; orbifold cohomology; quantum cohomology

Domaines: Géométrie algébrique [math.AG]

Samuel Boissiere, Etienne Mann, Fabio Perroni. The cohomological crepant resolution conjecture for P(1,3,4,4). International Journal of Mathematics, 2009, Vol. 20, (No. 6), pp.791-801. ⟨10.1142/S0129167X09005479⟩. ⟨hal-00124723⟩