Classifying birationally commutative projective surfaces

Details Classifying birationally commutative projective surfaces Classifying birationally commutative projective surfaces

2009-10-27

arxiv.org/abs/0910.5018v1

Mathematics

Rings and Algebras

60 pages; Proceedings of the LMS, 2011

Scientific paper

10.1112/plms/pdq054

Let R be a noetherian connected graded domain of Gelfand-Kirillov dimension 3 over an uncountable algebraically closed field. Suppose that the graded quotient ring of R is a skew-Laurent ring over a field; we say that R is a birationally commutative projective surface. We classify birationally commutative projective surfaces and show that they fall into four families, parameterized by geometric data. This generalizes work of Rogalski and Stafford on birationally commutative projective surfaces generated in degree 1; our proof techniques are quite different.

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