GK-dimension of birationally commutative surfaces

Details GK-dimension of birationally commutative surfaces GK-dimension of birationally commutative surfaces

2007-07-24

arxiv.org/abs/0707.3643v2

Mathematics

Rings and Algebras

26 pages, minor corrections from previous version based on referee report. To appear in Trans. Amer. Math. Soc

Scientific paper

Let k be an algebraically closed field, let K/k be a finitely generated field extension of transcendence degree 2 with automorphism sigma, and let A be an N-graded subalgebra of Q = K[t; sigma] with A_n finite dimensional over k for all n. Then if A is big enough in Q in an appropriate sense, we prove that GKdim A = 3,4,5 or is infinite, with the exact value depending only on the geometric properties of sigma. The proof uses techniques in the birational geometry of surfaces which are of independent interest.

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