Non-commutative ℙ¹-bundles over commutative schemes

Van den Bergh, M.

doi:10.1090/S0002-9947-2012-05469-9

Non-commutative $\mathbb {P}^1$-bundles over commutative schemes
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Trans. Amer. Math. Soc. 364 (2012), 6279-6313 Request permission

Abstract:

In this paper we develop the theory of non-commutative $\mathbb {P}^1$-bundles over commutative (smooth) schemes. Such non-commutative $\mathbb {P}^1$-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 $\mathbb {P}^1$-bundle over $\mathbb {P}^1$ in our sense.

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