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An Isaac Newton Institute Workshop

Trends in Noncommutative Geometry

Noncommutative Projective Surfaces

20th December 2006

Author: Daniel Rogalski (UCSD)

Abstract

We discuss recent work, joint with Toby Stafford, which describes a large class of noncommutative surfaces in terms of blowing up. Specifically, let A be a connected graded noetherian algebra, generated in degree 1, and suppose that the graded quotient ring Q(A) is of the form k(X)[t, t^-1; sigma] for some projective surface X with automorphism sigma. Then we prove that A can be written as a naive blowup of a projective surface Y birational to X. This enables one to obtain a deep understanding of the structure of such algebras.