Arrangements and beyond: Combinatorics, geometry, topology and applications

A vanishing result for the first twisted cohomology of affine varieties and applications to line arrangements

speaker: Pauline Bailet (Bremen University)

abstract: Let S be a smooth proper complex variety of dimension equal to or greater than 2, and let D= D₁ + ... + D_n a divisor on S (all D_i irreducible). Consider a rank one local system L on U=S\D, with monodromy t_i in C* around D_i. We give a general vanishing result for the first twisted cohomology group H¹(U,L), generalizing a result due to Cohen-Dimca-Orlik. Then we give some applications in the context of hyperplane arrangement, namely local system cohomology of line arrangement complements. In particular, we will apply our result to determine the monodromy action on the Milnor fiber of two hyperplane arrangements: the Ceva arrangement and the exceptional reflection arrangement of type G_{31}. (Joint work with A. Dimca and M. Yoshinaga)

timetable:
Tue 6 Jun, 14:30 - 15:10, Aula Dini
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