The Abelian/Nonabelian Correspondence and Frobenius Manifolds

Ionut Ciocan-Fontanine , Bumsig Kim , Claude Sabbah (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

We propose an approach via Frobenius manifolds to the study (began in math.AG/0407254) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding ''abelianized'' quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonabelian quotients are partial flag manifolds.

Domaines: Géométrie algébrique [math.AG]

Ionut Ciocan-Fontanine, Bumsig Kim, Claude Sabbah. The Abelian/Nonabelian Correspondence and Frobenius Manifolds. Inventiones Mathematicae, 2008, pp.301-343. ⟨hal-00854565⟩