Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)
By Antoine Douai, C. Sabbah. 2002
131 citations recorded by the source corpus.
This article explains a detailed example of the general result developed in the first part [3]. We were motivated by [1], where S. Barannikov describes a Frobenius structure attached to the Laurent polynomial f(u 0,..., u n ) = u 0 +...+ u n restricted to the torus U = {(u 0,..., u n ) ∈ ℂ n+1 | Π i u i = 1} and shows that it is isomorphic to the Frobenius structure attached to the quantum cohomology of the projective space ℙ n (ℂ) (as defined e.g., in [5]).
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a1708090c6cc58627926e3308039aa8e036f62fc
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In Geometry and Topology
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Citations in the corpus
- ORBIFOLD QUANTUM COHOMOLOGY OF WEIGHTED PROJECTIVE SPACES (2006, methodology): “ld a canonical Frobenius manifold on the base space of a universal unfolding for any Laurent polynomial which is convenient and non-degenerate with respect to its Newton polyhedron. In particular, in [DS04], the authors described explicitly this construction for the polynomial w 0u 0+···+wnun restri”
- An integral structure in quantum cohomology and mirror symmetry for toric orbifolds (2009, methodology): “See Sabbah [64] for an algebraic construction (for a tame function on an algebraic variety) using the Fourier-Laplace transform of the algebraic Gauß-Manin system (see also [65, 29]).”
- Quantum D-modules and generalized mirror transformations (2004, unknown): “In the literature, starting from a Laurent polynomial, Barannikov [3] (for P) and Douai and Sabbah [6, 7] (for weighted projective spaces or for a general tame function) constructed a Frobenius manifold of big quantum cohomology.”