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Résumé |
We consider the one parameter mirror family W of the quintic in P^4. By mirror symmetry the even Dp-brane
masses of the quintic M can be identified with four periods w.r.t to an integral symplectic basis of H_3(W,Z) at
the point of maximal unipotent monodromy. We establish that the masses of the D4 and D2 branes at the
conifold are given by the two algebraically independent values of the L-function of the weight four
holomorphic Hecke eigenform with eigenvalue one of \Gamma_0(25), that was found by Chad Schoen in this
context and whose coefficients a_p count the number of solutions of the mirror quinitic at the conifold over
the finite number field F_p as was discovered by del la Ossa, Candelas and Villegas. Using the theory of
periods and quasi-periods of \Gamma_0(N) and the special geometry pairing on Calabi-Yau 3 folds we can fix
further values in the connection matrix between the maximal unipotent monodromy point and the conifold
point. |
