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
Gauged linear sigma models and
non-complete-intersection 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 well-studied both in mathematics and in physics, in
part because of Witten's "gauged linear sigma model" (GLSM) construction which
provides a two-dimensional 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 well-understood that "most"
varieties are not complete intersections. A classical result of Serre shows that a

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

Collections: Mathematics