Soit X une courbe projective lisse et irréductible munie d'une involution σ. Dans cette thèse, nous étudions les fibrés vectoriels invariants and anti-invariants sur X sous l'action induite par σ. On introduit la notion de modules σ-quadratiques et on l'utilise, avec GIT, pour construire ces espaces de modules, puis on en étudie certaines propriétés. Ces espaces de modules correspondent aux espaces de modules de G-torseurs parahoriques sur la courbe X/σ , pour certains schémas en groupes parahoriques G de type Bruhat-Tits, qui sont twistés dans le cas des anti-invariants. Nous développons les systèmes de Hitchin sur ces espaces de modules et on les utilise pour dériver une classification de leurs composantes connexes en les dominant par des variétés de Prym. On étudie aussi le fibré déterminant sur les espaces de modules des fibrés vectoriels anti-invariants. Dans certains cas, ce fibré en droites admet certaines racines carrées appelées fibrés Pfaffiens. On montre que les espaces des sections globales des puissances de ces fibrés en droites (les espaces des fonctions thêta généralisées) peuvent être canoniquement identifier avec les blocs conformes associés aux algèbres de Kac-Moody affines twistées de type A(2). / Let X be a smooth irreducible projective curve with an involution σ. In this dissertation, we studythe moduli spaces of invariant and anti-invariant vector bundles over X under the induced action of σ. We introduce the notion of σ-quadratic modules and use it, with GIT, to construct these moduli spaces, and than we study some of their main properties. It turn out that these moduli spaces correspond to moduli spaces of parahoric G-torsors on the quotient curve X/σ, for some parahoric Bruhat-Tits group schemes G, which are twisted in the anti-invariant case.We study the Hitchin system over these moduli spaces and use it to derive a classification of theirconnected components using dominant maps from Prym varieties. We also study the determinant of cohomology line bundle on the moduli spaces of anti-invariant vector bundles. In some cases this line bundle admits some square roots called Pfaffian of cohomology line bundles. We prove that the spaces of global sections of the powers of these line bundles (spaces of generalized theta functions) can be canonically identified with the conformal blocks for some twisted affine Kac-Moody Lie algebras of type A(2).

The dissertation introduces the art performance by Miroslav Hornicek. It reflects the collage creation which Miroslav Hornicek devoted more than twenty years. The author introduced the gift of improvisation and humor into his collage. Many of them look like graphic, some of them remind the theater scene. He often repeats the same motive such as eye, sisters, theatrical costumes, sculptures, senses and body organs. It is interesting that despite his work he did not consider himself like the artist. He created many collage, he found inspiration in the creation of Max Ernst, Toyen, Jindrich Styrsky and Jiri Kolar. In relating with Jiri Kolar it is possible to search a certain similarity. From the poet became the artist, collage maker. Miroslav Hornicek was primarily the actor who has also found a way of life in creating collages. Miroslav Hornicek wrote to some of his collages names and interpretations. This material is very important for trying to understand his theater scenes and a tangle of something "incomprehensible", because of collages effect on the viewer. Finally, the dissertation aims to look at his art creation as a whole, highlight the exhibition activity and introduce Miroslav Hornicek not only as the actor, writer, dramatist, director and also the artist with an incredible imagination...