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Comparison of rapid decay homology theories and construction of solution basis of irregular connections of hypergeometric type

Le : 17/01/2017 16h45
Par : S.J. Matsubara-Heo (Tokyo)
Lieu : I 001
Lien web :
Résumé : In 2009, M. Hien introduced rapid decay homology group associated to an irregular connection on a smooth complex affine variety, and showed that it is the dual group of the algebraic de Rham cohomology group. On the other hand, F. Pham has already introduced his version of rapid decay homology when the connection is the so-called elementary irregular connection in 1985. In this talk, we will give a geometric proof of the comparison theorem. The key ingredient is the construction of a suitable vector field on the oriented blow up. (The comparison of these homology theories was essentially proved by C. Sabbah by means of D-modules, but it is not parallel to our proof.) As applications, we construct a solution basis of two irregular connections. One comes from a hyperplane arrangement which is not necessarily generic, the other comes from a generic hypersphere arrangement of K. Aomoto.