 
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 SeibergWitten 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 Ftheory, 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 SeibergWitten
curve for pure SU(2) gauge theory. By carrying out a base transformation, one obtains
a 3parameter family of elliptically fibered K3 surfaces. The gauge theoretic relation
between the SeibergWitten curves with Nf = 2 and Nf = 0 hypermultiplets in
turn defines a ShiodaInose structure on each K3 surface in the family with quotient
birational to a Kummer surface of the Jacobian of a genustwo curve.
