On monodromy representation of period integrals associated to an algebraic curve with bi-degree (2,2)


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TANABE S.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.25, sa.1, ss.207-231, 2017 (SCI-Expanded) identifier identifier

Özet

We study a problem related to Kontsevich's homological mirror symmetry conjecture for the case of a generic curved with bi-degree (2,2) in a product of projective lines P-1 x P-1. We calculate two differenent monodromy representations of period integrals for the affine variety x((2,2)) obtained by the dual polyhedron mirror variety construction from y. The first method that gives a full representation of the fundamental group of the complement to singular loci relies on the generalised Picard-Lefschetz theorem. The second method uses the analytic continuation of the Mellin-Barnes integrals that gives us a proper subgroup of the monodromy group. It turns out both representations admit a Hermitian quadratic invariant form that is given by a Gram matrix of a split generator of the derived category of coherent sheaves on on Id with respect to the Euler form.