Rogalski, D. and Stafford, J T (2007) A class of noncommutative projective surfaces. [MIMS Preprint]
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Abstract
Let A=k+A_1+A_2.... be a connected graded, noetherian k-algebra that is generated in degree one over an algebraically closed field k. Suppose that the graded quotient ring Q(A) has the form Q(A)=k(Y)[t,t^{-1},sigma], where sigma is an automorphism of the integral projective surface Y. Then we prove that A can be written as a naive blowup algebra of a projective surface X birational to Y. This enables one to obtain a deep understanding of the structure of these algebras; for example, generically they are not strongly noetherian and their point modules are not parametrized by a projective scheme. This is despite the fact that the simple objects in the quotient category qgr A will always be in (1-1) correspondence with the closed points of the scheme X.
Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | {Noncommutative projective geometry, noncommutative surfaces, noetherian graded rings, naive blowing~up |
Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras |
Depositing User: | Professor J T Stafford |
Date Deposited: | 26 Nov 2007 |
Last Modified: | 08 Nov 2017 18:18 |
URI: | http://eprints.maths.manchester.ac.uk/id/eprint/963 |
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- A class of noncommutative projective surfaces. (deposited 26 Nov 2007) [Currently Displayed]
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