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Session

D-M3: D-Modules: Bridging Theory and Applications Location: M630 Session Chair: Andreas Hohl Session Chair: Anna-Laura Sattelberger

Presentation 1

Logarithmic Gauss-Manin connections and nearby cycle functors Henry Dakin TU Chemnitz, Germany Given a divisor on a complex manifold, we show that the monodromy automorphism of the associated logarithmic Gauss-Manin connection is given by taking residues of relative logarithmic forms along said divisor, extending a result of Steenbrink in the case of simple normal crossing divisors. When the divisor satisfies the twisted logarithmic comparison theorem, we show that this is in turn equal to the monodromy automorphism on the nearby cycles functor along the divisor.