Structures différentielles en géométrie algébrique

Druel, Stéphane

Directeur de thèse : Beauville, Arnaud

Membres du jury : Beauville, Arnaud ; Le Potier, Joseph ; Peternell, Thomas ; Raynaud, Michel ; Voisin, Claire

Thèses d'Orsay, no. 573 (2000) , 86 p.

Résumé

This thesis deals on the one hand with some differential structures on algebraic varieties and on the other hand with sheaves on cubic hypersurfaces in the four dimentional projective space.

In a first part, we give a complete description of non trivial quasi-regular Poisson structures on projective threefolds.

The second part is devoted to contact structures on toric varieties and the third one to contact structures on projective five dimensional manifolds. We show furthermore that a contact manifold has negative Kodaira dimension.

In the fourth part, we describe projective manifolds whose tangent bundle split as a direct sum of line bundles with the assumption that the direct summands are integrable.

Finally, in the fifth part, we show that the moduli space of rank two semistable sheaves on a cubic threefold, with trivial first and third Chern classes and with second Chern class twice the class of a line, is isomorphic to the blow up of the intermediate Jacobian of the aforesaid cubic along a smooth surface.

Classification : 14D20, 14F05, 14J10, 14J60, 14K30, 14M25, 53D10, 53D17
Mots-clés : Algebraic geometry, Poisson manifolds, Contact manifolds, Toric varieties, Mori theory, Vector bundles, Moduli spaces, Intermediate Jacobians

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     author = {Druel, St\'ephane},
     title = {Structures diff\'erentielles en g\'eom\'etrie alg\'ebrique},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris-Sud U.F.R. Scientifique d'Orsay},
     number = {573},
     year = {2000},
     language = {fr},
     url = {http://www.numdam.org/item/BJHTUP11_2000__0573__A1_0/}
}

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Druel, Stéphane. Structures différentielles en géométrie algébrique. Thèses d'Orsay, no. 573 (2000), 86 p. http://numdam.org/item/BJHTUP11_2000__0573__A1_0/

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