Thèse de doctorat en Mathématiques
Sous la direction de Viatcheslav Kharlamov.
Soutenue en 2004
Structures réelles sur les variétés toriques compactes
Pas de résumé disponible.
In this thesis we study real structures on compact toric varieties. After proving that their number (up to conjugation) is finite, we limit ourselves to toric real structures i. E. , real structures that normalize the action of the torus and define equivalencies between them. Then we calculate an upper bound of the number of non-equivalent such structures. We list explicitely the groups generated by toric real structures in dimension 2 and 3 and determine some minimal models for surfaces. We are also interested in the real toric variety. We prove that it is pathwise-connected when it is non-empty and give the complete list of its topological types in case of surfaces and fano-threefolds. We end this work by the application to the toric threefolds equipped with their canonical real structures of a Kollar's conjecture:Is a real hyperbolic connected treefold the real part of some complex projective rational variety ?