A class of noncommutative projective surfaces

D. Rogalski, J. T. Stafford

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Let A=⊕i≥0 Ai 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(X)[t, t-1; σ], where σ is an automorphism of the integral projective surface X. Then we prove that A can be written as a naïve blowup algebra of a projective surface X birational to X. 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 qgr-A will always be in (1-1) correspondence with the closed points of the scheme X. © 2009 London Mathematical Society.
    Original languageEnglish
    Pages (from-to)100-144
    Number of pages44
    JournalProceedings of the London Mathematical Society
    Volume99
    Issue number1
    DOIs
    Publication statusPublished - Jul 2009

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