ARITHMETIC GEOMETRY LEARNING SEMINAR
Time: Wednesday, 11:30-1:30pm
Location: MATH 731
January 24 th: Feng Hao
Title: An algebraic introduction to Gauss-Manin connection
(by Katz and Oda)
Abstract: In this presentation, I will give a purely algebraic construction of Gauss-Manin connection arising from a smooth morphism $f: X \rightarrow Y$ between two smooth schemes over $k$, which is realized as a connection differential in the first page of certain spectral sequence. Then using Cech cohomology calculation, I will show that it is exactly the one Manin originally defined, as a connecting morphism in a long exact sequence of hyper-higher direct image sheaves of a certain short exact sequence De Rham complexes of the morphism $f$.
February 7: Pavel Coupek
Title: Existence of Lefschetz pencils
Abstract: A Lefschetz pencil for a variety X is a tool that allows one to fibre X over the projective line (after a blowup) in a way that the non-smooth fibres have a unique quadratic singularity. In the presentation, I will discuss the proof of existence of Lefschetz pencils for smooth projective varieties in characteristic 0.