Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Noncommutative Minimal Surfaces   In the ongoing programme to classify noncommutative projective surfaces
(connected graded noetherian domains of Gelfand-Kirillov dimension three) a
natural question is to determine the minimal models within any birational
class. In this paper we show that the generic noncommutative projective plane
(corresponding to the three dimensional Sklyanin algebra R) as well as
noncommutative analogues of P^1 x P^1 and of the Hirzebruch surface F_2
(arising from Van den Bergh's quadrics R) satisfy very strong minimality
conditions. Translated into an algebraic question, where one is interested in a
maximality condition, we prove the following theorem. Let R be a Sklyanin
algebra or a Van den Bergh quadric that is infinite dimensional over its centre
and let A be any connected graded noetherian maximal order containing R, with
the same graded quotient ring as R. Then, up to taking Veronese rings, A is
isomorphic to R. Secondly, let T be an elliptic algebra (that is, the
coordinate ring of a noncommutative surface containing an elliptic curve).
Then, under an appropriate homological condition, we prove that every connected
graded noetherian overring of T is obtained by blowing down finitely many lines
(line modules).

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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: physics