Non-commutative $\PP^1$-bundles over commutative schemes

Michel Van den Bergh

Non-commutative $\PP^1$-bundles over commutative schemes

Rings and Algebras 2010-09-24 v3 Algebraic Geometry

Authors: Michel Van den Bergh

Abstract

In this paper we develop the theory of non-commutative $\PP^1$ -bundles over commutative (smooth) schemes. Such non-commutative $\PP^1$ -bundles occur in the theory of $D$ -modules but our definition is more general. We can show that every non-commutative deformation of a Hirzebruch surface is given by a non-commutative $\PP^1$ -bundle over $\PP^1$ in our sense.

Keywords

noncommutative geometry

Cite

@article{arxiv.math/0102005,
  title  = {Non-commutative $\PP^1$-bundles over commutative schemes},
  author = {Michel Van den Bergh},
  journal= {arXiv preprint arXiv:math/0102005},
  year   = {2010}
}

Comments

Corrections suggested by the referee implemented. To appear in Transactions of the AMS

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