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Invariant of the hypergeometric group associated to the quantum cohomology of the projective space. (English) Zbl 1073.32014
Summary: We present a simple method to calculate the Stokes matrix for the quantum cohomology of the projective spaces \(\mathbb C \mathbb P^{k-1}\) in terms of certain hypergeometric group. We present also an algebraic variety whose fibre integrals are solutions to the given hypergeometric equation.

32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
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[1] Balser, W.; Jurkat, W.B.; Lutz, D.A.; Balser, W.; Jurkat, W.B.; Lutz, D.A., On the reduction of connection problems for differential equations with an irregular singular point to ones with only regular singularities, I, II, SIAM J. math. anal, SIAM J. math. anal, 19, 2, 398-443, (1988) · Zbl 0639.34034
[2] Barannikov, S., Semi-infinite Hodge structures and mirror symmetry for projective spaces · Zbl 1304.58003
[3] Beilinson, A.A., Coherent sheaves on cpn and problems of linear algebra, Funct. anal. appl, 13, 2, 68-69, (1978) · Zbl 0402.14006
[4] Beukers, F.; Heckman, G., Monodromy for the hypergeometric function _nfn−1, Invent. math, 95, 325-354, (1989) · Zbl 0663.30044
[5] Dubrovin, B., Painlevé transcendents in two dimensional topological field theory, (), 287-412 · Zbl 1026.34095
[6] Dubrovin, B., Geometry and analytic theory of Frobenius manifolds, (), 315-326 · Zbl 0916.32018
[7] Givental’, A., Equivariant Gromov-Witten invariants, Intern. math. res. notices, 13, 613-663, (1996) · Zbl 0881.55006
[8] Golyshev, V.V., Riemann-Roch variations, Izv. math, 65, 5, 853-887, (2001) · Zbl 1068.14047
[9] A.L. Gorodentsev, S.A. Kuleshov, Helix theory, MPIM preprint series 97, 2001
[10] Greuel, G.-M., Der Gauss-Manin zusammenhang isolierter singularitäten von vollständigen durchschnitten, Math. ann, 214, 3, 235-266, (1975) · Zbl 0285.14002
[11] Guzzetti, D., Stokes matrices and monodromy of the quantum cohomology of projective spaces, Comm. math. phys, 207, 2, 341-383, (1999) · Zbl 0976.53094
[12] Kontsevich, M., Homological algebra of mirror symmetry, (), 120-139 · Zbl 0846.53021
[13] Levelt, A.H.M., Hypergeometric functions, Indag. math, 23, 361-403, (1961)
[14] Okubo, K.; Okubo, K., Connection problems for systems of linear differential equations, (), 238-248, (1987), Tokyo Metropolitan University · Zbl 0633.15013
[15] S. Tanabé, Transformée de Mellin des intégrales - fibres associées à l’intersection complète non-dégénérée, Math. AG/0405399
[16] Zaslow, E., Solitons and helices: the search for a math-phys bridge, Comm. math. phys, 175, 337-375, (1996) · Zbl 0851.53055
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