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Géométrie de quelques algèbres et théorèmes d'annulation

Abstract : Zak's theorem shows a rather mysterious link between algebraic objects, Jordan algebras, and objets appearing naturally in complex projective geometry, Scorza varieties. I give variations of the proof of Zak's theorem which explain directly this link. To this end, I define the Jordan algebra associated with a Scorza variety by projective geometry constructions; I also give a similar definition of the algebra of matrices, of Lie algebras and of composition algebras, which allows one to provide a geometric proof of some algebraic results. On the other way, I prove vanishing theorems for ample vector bundles. I give a generalisation of a theorem by Laytimi and Nahm, and results for vector bundles with small rank. They imply a small part of a conjecture by Fulton and Lazarsfeld about connectivity of degeneracy loci of a vector bundle morphism.
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Contributor : Arlette Guttin-Lombard <>
Submitted on : Thursday, October 14, 2004 - 9:17:00 AM
Last modification on : Wednesday, November 4, 2020 - 2:05:33 PM
Long-term archiving on: : Thursday, September 13, 2012 - 12:15:24 PM


  • HAL Id : tel-00007115, version 1



Pierre-Emmanuel Chaput. Géométrie de quelques algèbres et théorèmes d'annulation. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2003. Français. ⟨tel-00007115⟩



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