Quantum Toric Varieties

Colin Ingalls

Abstract: Given a toric variety of dimension $n$ we construct a natural flat family of noncommutative varieties with base a torus of dimension $n(n-1)/2$. The original commutative variety is the fibre over the identity element of the torus. We study the centres and open and closed subvarieties of the fibres of the families. The centre is interpreted as a torus group quotient of the original variety. The irreducible subvarieties correspond to prime ideals in noncommutative tori orbits. We prove a generalization of Hochster's theorem and the Picard group of bimodules is determined for a sufficiently general member of the family.

created Mon Mar 20 12:48:52 PST 2000