The subject of this paper is the big quantum cohomology rings of symplectic isotropic Grassmannians IG(2, 2n). We show that these rings are regular. In particular, by "generic smoothness", we obtain a conceptual proof of generic semisimplicity of the big quantum cohomology for IG(2, 2n). Further, by a general result of C. Hertling, the regularity of these rings implies that they have a description in terms of isolated hypersurface singularities, which we show in this case to be of type A n−1 . By the homological mirror symmetry conjecture, these results suggest the existence of a very special full exceptional collection in the derived category of coherent sheaves on IG(2, 2n). Such a collection is constructed in the appendix by Alexander Kuznetsov.

The classical Stokes matrices for the quantum differential equation of P n are computed using multisummation and the 'monodromy identity'. Thus, we recover the results of D. Guzzetti that confirm Dubrovin's conjecture for projective spaces. The same method yields explicit formulas for the Stokes matrices of the quantum differential equations of smooth Fano hypersurfaces in P n and for weighted projective spaces. Keywords Stokes matrices • Quantum cohomology • Monodromy identity • Quantum differential equations Mathematics Subject Classification 34M40 • 53D45 Originally since May 2013 the paper had been processed by the Central European Journal of Mathematics but it was withdrawn in April 2014 due to imposition of publishing fees and resubmitted to the European Journal of Mathematics.

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In this note we introduce the concept of F-algebroid, and give its elementary properties and some examples. We provide a description of the almost duality for Frobenius manifolds, introduced by Dubrovin, in terms of a composition of two anchor maps of a unique cotangent F-algebroid.

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