中科院数学与系统科学研究院

数学研究所

学术报告会

报告人：Michael Temkin（耶路撒冷希伯莱大学）

题  目：Logarithmic resolution of singularities

时  间：2017.10.11（星期三），16 :30-17:30

地  点：数学院南楼N913室

摘  要：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.