 
Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY ˇ DAVIS ˇ IRVINE ˇ LOS ANGELES ˇ MERCED ˇ RIVERSIDE ˇ SAN DIEGO ˇ SAN FRANCISCO
CSANTA BARBARA ˇ SANTA CRUZ
Geometry, Topology, and Physics Seminar
Gauged linear sigma models and
noncompleteintersection CalabiYau varieties
Dave Morrison
UCSB
Friday, January 28, 2011, 4:00 p.m.
Room 6635 South Hall
Abstract: A large class of examples of CalabiYau varieties is provided by
"complete intersections" in toric Fano varieties: that is, CalabiYau varieties whose
homogeneous ideal has the same number of generators as the codimension of the
variety. This class has been wellstudied both in mathematics and in physics, in
part because of Witten's "gauged linear sigma model" (GLSM) construction which
provides a twodimensional superconformal field theory corresponding to the Calabi
Yau variety. The GLSM corresponding to a complete intersection always has an
abelian gauge group.
From the viewpoint of projective geometry, it is wellunderstood that "most"
varieties are not complete intersections. A classical result of Serre shows that a
