Rogalski, D. and Stafford, J T (2009) A class of noncommutative projective surfaces. Proc London Math Soc, 99. pp. 100144. ISSN 17499097
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Abstract
Let A=k+A_1+A_2.... be a connected graded, noetherian kalgebra 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 (11) correspondence with the closed points of the scheme X.
Item Type:  Article 

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:  15 May 2013 
Last Modified:  20 Oct 2017 14:13 
URI:  http://eprints.maths.manchester.ac.uk/id/eprint/1975 
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A class of noncommutative projective surfaces. (deposited 26 Nov 2007)
 A class of noncommutative projective surfaces. (deposited 15 May 2013) [Currently Displayed]
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