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An ampleness criterion for rank 2 vector bundles on surfaces

Abstract : We observe that the proof of the Bogomolov stable restriction theorem can be adapted to give an ampleness criterion for globally generated rank 2 vector bundles on certain surfaces. This applies to the Lazarsfeld-Mukai bundles, to congruences of lines in P^3, and possibly to the construction of surfaces with ample cotangent bundle (help welcome!).
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https://hal.archives-ouvertes.fr/hal-02509864
Contributor : Arnaud Beauville <>
Submitted on : Tuesday, March 17, 2020 - 11:35:10 AM
Last modification on : Monday, October 12, 2020 - 10:27:34 AM

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  • HAL Id : hal-02509864, version 1
  • ARXIV : 1806.00243

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Arnaud Beauville. An ampleness criterion for rank 2 vector bundles on surfaces. Vietnam Journal of Mathematics, Springer, 2020. ⟨hal-02509864⟩

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