Speaker: Susan Sierra, University of Edinburgh

Title: Noncommutative rational surfaces

 

Abstract: We report on ongoing work to understand noncommutative graded rings which have the same quotient division ring as the Sklyanin algebra, which is often thought of as a "noncommutative P^2". We give a noncommutative version of Castelnuovo's classic theorem that (-1) lines on a smooth surface can be contracted, and show how this may be used to construct an explicit birational map between a noncommutative P2 and a noncommutative quadric surface. This has applications to the classification of noncommutative projective surfaces, one of the major open problems in noncommutative algebraic geometry. The talk is based on joint work with Rogalski and Stafford.