## 2007.213: A class of noncommutative projective surfaces

2007.213:
D. Rogalski and J T Stafford
(2007)
*A class of noncommutative projective surfaces.*

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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 2000 > 14 Algebraic geometry MSC 2000 > 16 Associative rings and algebras |

MIMS number: | 2007.213 |

Deposited By: | Professor J T Stafford |

Deposited On: | 26 November 2007 |

### Available Versions of this Item

- A class of noncommutative projective surfaces (deposited 15 May 2013)
- A class of noncommutative projective surfaces (deposited 26 November 2007)
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- A class of noncommutative projective surfaces (deposited 26 November 2007)

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