Toric Geometry

Friday, April 13, 2007 - 2:00pm - 3:30pm
EE/CS 3-180
Diane Maclagan (Rutgers, The State University Of New Jersey )
This talk gives a brief introduction to the theory of toric
varieties. In the first half of the talk I give seven different
definitions of a toric variety and compare them briefly. In the second
half I describe some of the uses of toric varieties. The first of these
is as a testing ground for algebraic geometric conjectures, as many
geometric questions about toric varieties can be turned into combinatorial
questions. A second use is as a good ambient variety in which to embed
and study other varieties, using the fact that smooth toric varieties are
natural generalizations of projective space.