Complements of hyperplane sub-bundles in projective space bundles over the projective line

Abstract : We establish that the isomorphy type as an abstract algebraic variety of the complement of an ample hyperplane sub-bundle H of a projective space bundle of rank r-1 over the projective line depends only on the the r-fold self-intersection of H . In particular it depends neither on the ambient bundle nor on a particular ample hyperplane sub-bundle with given r-fold self-intersection. Our proof exploits the unexpected property that every such complement comes equipped with the structure of a non trivial torsor under a vector bundle on the affine line with a double origin.
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https://hal.archives-ouvertes.fr/hal-00618025
Contributor : Adrien Dubouloz <>
Submitted on : Wednesday, August 31, 2011 - 2:08:55 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Thursday, December 1, 2011 - 2:26:24 AM

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  • HAL Id : hal-00618025, version 1
  • ARXIV : 1108.6209

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Adrien Dubouloz. Complements of hyperplane sub-bundles in projective space bundles over the projective line. 2011. ⟨hal-00618025⟩

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