Quantum cohomology of the Grassmannian and alternate Thom-Sebastiani

Abstract

We introduce the notion of alternate product of Frobenius manifolds and we give, after [math.AG/0610265], an interpretation of the Frobenius manifold structure canonically attached to the quantum cohomology of G(r,n+1) in terms of alternate products. We also investigate the relationship with the alternate Thom-Sebastiani product of Laurent polynomials.

29 pages. Revised version: Corollary 1.9 corrected, minor mistakes corrected, few typos corrected

References in corpus (7)

• Hypergeometric periods for a tame polynomial
• The Abelian/Nonabelian Correspondence and Frobenius Manifolds
• Semi-infinite Hodge structures and mirror symmetry for projective spaces
• Cohomologie quantique orbifolde des espaces projectifs a poids
• The Sebastiani-Thom Isomorphism in the Derived Category
• Semicontinuity of the spectrum at infinity
• The tensor product in the theory of Frobenius manifolds

Cited by in corpus (5)

• Gamma classes and quantum cohomology of Fano manifolds: Gamma conjectures
• Helix Structures in Quantum Cohomology of Fano Varieties
• Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers
• Gromov-Witten Invariants of Local P^2 and Modular Forms
• Deresonating a Tate period