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Algebraic Geometry: "Applications of some double covers of a class of surfaces of general type"

Dr. Christopher Lyons, CSU Fullerton

Thursday, March 9, 2017
  1:10–2 p.m.

Location: Surge Building 268
  Parking Information

Category: Seminar

Description: We will focus on complex algebraic surfaces with invariants p_g=q=1 and K^2=2, an interesting class of surfaces of general type first classified in the late 1970s by Bombieri-Catanese and Horikawa. Inspired by work of Ishida, we describe how to obtain polynomial equations for unramified double covers of these surfaces. These more accessible double covers allow one to obtain results about the original surfaces themselves. First we will discuss how one may obtain (via zeta functions) an explicit surface with p_g=q=1, K^2=2 having minimal Picard number. This result and others then contribute towards proofs about the larger family of surfaces with these invariants, such as a big monodromy theorem and the Tate Conjecture in characteristic zero. This is joint work with Paul Lewis.

Additional Information: AG Seminar

Open to: General Public
Admission: Free
Sponsor: Mathematics

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