Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series MATH-IHES
Subjects hep-th
Date Wednesday 11 October 2017
Time 10:30
Institute IHES
Seminar Room Centre de conférences Marilyn et James Simons
Speaker's Last Name Temkin
Speaker's First Name M.
Speaker's Email Address
Speaker's Institution The Hebrew University of Jerusalem & IHES
Title Logarithmic resolution of singularities
Abstract The famous Hironaka's theorem asserts that any integral algebraic variety X of characteristic zero can be modified to a smooth variety X_res by a sequence of blowings up. Later it was shown that one can make this compatible with smooth morphisms Y → X in the sense that Y_res → Y is the pullback of X_res → X. In a joint project with D. Abramovich and J. Wlodarczyk, we construct a new algorithm which is compatible with all log smooth morphisms (e.g. covers ramified along exceptional divisors). We expect that this algorithm will naturally extend to an algorithm of resolution of morphisms to log smooth ones. In particular, this should lead to functorial semistable reduction theorems. In my talk I will tell about main ideas of the classical algorithm and will then discuss logarithmic and stack-theoretic modifications we had to make in the new algorithm.
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