ON ALMOST DUALITY FOR FROBENIUS MANIFOLDS

By Boris Dubrovin. 2003

149 citations recorded by the source corpus.

We present a universal construction of almost duality for Frobenius man- ifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We illustrate the general considerations by exam- ples from the singularity theory, mirror symmetry, the theory of Coxeter groups and Shephard groups, from the Seiberg - Witten duality.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/865c17b2f0d099bb9a644eb603529ffb73cc9332

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Relations in the tautological ring of the moduli space of curves (2013, methodology): “For Witten’s class, the Frobenius manifold coincides with the canonical Frobenius structure on the versal deformation of the Ar−1 singularity [7] up to a coordinate change.”
THE CURVATURE OF A HESSIAN METRIC (2004, background): “…ask if the forms we have found, together with Dubrovin’s example of the Maschke sextic (([7], Corollary 5.9 and Example 3), are essentially the only ones for which the Hessian metric is flat: Question 6.2 Let f be a ternary form of degree d over C whose Hessian determinant is not identically zero.”
Relations on Mbar_{g,n} via 3-spin structures (2013, unknown): “For Witten’s class, the Frobenius manifold coincides with the canonical Frobenius structure on the versal deformation of the A r − 1 singularity [4] up to a coordinate change.”