GK-dimension of birationally commutative surfaces

Author:
D. Rogalski

Journal:
Trans. Amer. Math. Soc. **361** (2009), 5921-5945

MSC (2000):
Primary 14A22, 14E05, 16P90, 16S38, 16W50

Published electronically:
June 15, 2009

MathSciNet review:
2529919

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Abstract: Let be an algebraically closed field, let be a finitely generated field extension of transcendence degree , let , and let be an -graded subalgebra with for all . Then if is big enough in in an appropriate sense, we prove that or , with the exact value depending only on the geometric properties of . The proof uses techniques in the birational geometry of surfaces which are of independent interest.

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Additional Information

**D. Rogalski**

Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112

Email:
drogalsk@math.ucsd.edu

DOI:
https://doi.org/10.1090/S0002-9947-09-04885-5

Keywords:
GK-dimension,
graded rings,
noncommutative projective geometry,
noncommutative surfaces,
birational geometry

Received by editor(s):
September 19, 2007

Published electronically:
June 15, 2009

Additional Notes:
The author was partially supported by the NSF through grants DMS-0202479 and DMS-0600834.

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.