Mixed Frobenius Structure and Local A-model

Abstract

We define the notion of mixed Frobenius structure which is a generalization of the structure of a Frobenius manifold. We construct a mixed Frobenius structure on the cohomology of weak Fano toric surfaces and that of the three dimensional projective space using local Gromov-Witten invariants. This is an analogue of the Frobenius manifold associated to the quantum cohomology in the local Calabi-Yau setting.

(v3) 35 pages, version to appear in Kyoto Journal of Mathematics

References in corpus (4)

• A New Cohomology Theory for Orbifold
• The orbifold Chow ring of toric Deligne-Mumford stacks
• Enumerative geometry of Calabi-Yau 4-folds
• Mixed trTLEP-structures and mixed Frobenius structures