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Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY · DAVIS · IRVINE · LOS ANGELES · MERCED · RIVERSIDE · SAN DIEGO · SAN FRANCISCO
CSANTA BARBARA · SANTA CRUZ
Geometry, Topology, and Physics Seminar
Kummer surfaces from Seiberg-Witten curves
Andreas Malmendier
UCSB
Friday, October 9th, 2009, 4:00 p.m.
Room 6635 South Hall
Abstract:Jacobian elliptic surfaces are elliptic surfaces with sections. They play a
key role in gauge theory as well as in string theory. In gauge theory, the Seiberg-
Witten curve of SU(2) gauge theory arises as a pencil generated by two cubics in
the plane forming a rational elliptic surface. In F-theory, K3 surfaces constructed as
elliptic surfaces with sections are also of special importance.
In my talk, I will start with the Weierstrass normal form of the Seiberg-Witten
curve for pure SU(2) gauge theory. By carrying out a base transformation, one obtains
a 3-parameter family of elliptically fibered K3 surfaces. The gauge theoretic relation
between the Seiberg-Witten curves with Nf = 2 and Nf = 0 hypermultiplets in
turn defines a Shioda-Inose structure on each K3 surface in the family with quotient
birational to a Kummer surface of the Jacobian of a genus-two curve.
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