Abhyankar's conjecture on Galois groups over curves.
About Abhyankar's conjectures on space lines
About -bundles over elliptic curves
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.
About some Riemann surfaces and plane tilings.
About the group law for the Jacobi variety of a hyperelliptic curve.
About the Witt rings of function fields of algebroid quadratic quasihomogeneous surfaces.
ACM embeddings of curves of a quadric surface
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.
Action du groupe de Galois sur les périodes de certaines courbes de Mumford
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...
Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero
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 .
Addendum 7.1.1981. Correzione a "su una congettura di Petri".
Addendum and errata “Hyperbolic tessellations, modular symbols, and elliptic curves over complex quadratic fields”
Addendum : Propriétés de descente des variétés à fibré cotangent ample
Addendum zu: Quasi-Frobenius-Algebren und lokal vollständige Durchschnitte:
Admissible pairing on a curve.
Affine coordinates for Teichmüller spaces.
Affine Curves in Characteristic p.
Affine Curves in Characteristic p are Set Theoretic Complete Intersections.
Affine Gelfand-Dickey Brackets and Holomorphic Vector Bundles.
Affine lines on logarithmic Q-homology planes.
Affine plane curves with one place at infinity
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.