UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

November 17, 2009

939 Evans Hall


3:45PM: Elliptic K3 surfaces, p-torsion sections and wild automorphisms

Christian Liedtke

3 surfaces are a class of surfaces that naturally generalize the class of elliptic curves. Some of them admit maps to the projective line whose fibers are elliptic curves---these are called elliptic fibrations. Sections of such a fibration can be multiplied using the group law on the fibers. I'll explain what happens in characteristic p when there is a section of order p^n for some n, and how this is related to Igusa curves -- the characteristic p analog of modular curves. Using this we get explicit equations for such surfaces. In particular, we can check arithmetic conjectures and find beautiful connections between arithmetic and geometry.

5:00PM: TBA

David Berlekamp

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