Let be a complex algebraic group, simple and simply connected, a maximal torus and the Weyl group. One shows that the coarse moduli space parametrizing -equivalence classes of semistable -bundles over an elliptic curve is isomorphic to . By a result of Looijenga, this shows that is a weighted projective space.
Let C be a smooth integral projective curve admitting two pencils ga1 and gb1 such that ga1 + gb1 is birational. We give conditions in order that the complete linear system |sga1 + rgb1| be normally generated or very ample.
Nous étudions l’action du groupe de Galois sur les périodes des courbes de Mumford qui sont des revêtements cycliques de . Lorsque le degré de ce revêtement est premier à la caractéristique résiduelle du corps de base, nous décomposons le réseau des périodes en une somme directe de modules monogènes, le nombre de ces modules monogènes étant déduit de la géométrie de la courbe (théorème 4). Ceci nous permet de donner une condition nécessaire et suffisante pour que le module des périodes soit libre...
In this paper we establish the action of the Grothendieck-Teichmüller group on the prime order torsion elements of the profinite fundamental group . As an intermediate result, we prove that the conjugacy classes of prime order torsion of are exactly the discrete prime order ones of the .
In this paper we give a new algebro-geometric proof to the semi-group theorem due to Abhyankar-Moh for the affine plane curves with one place at infinity and its inverse theorem due to Sathaye-Stenerson. The relations between various invariants of these curves are also explained geometrically. Our new proof gives an algorithm to classify the affine plane curves with one place at infinity with given genus by computer.