Curves on surfaces with multiple line.
Curves with finite turn
In this paper we study the notions of finite turn of a curve and finite turn of tangents of a curve. We generalize the theory (previously developed by Alexandrov, Pogorelov, and Reshetnyak) of angular turn in Euclidean spaces to curves with values in arbitrary Banach spaces. In particular, we manage to prove the equality of angular turn and angular turn of tangents in Hilbert spaces. One of the implications was only proved in the finite dimensional context previously, and equivalence of finiteness...
Curves with Invertible Hasse-Witt-Matrix.
Curves with only triple ramification
We show that the set of smooth curves of genus admitting a branched covering with only triple ramification points is of dimension at least . In characteristic two, such curves have tame rational functions and an analog of Belyi’s Theorem applies to them.
Cusp algebras.
Cuspidal Projections of Space Curves.
Cutting diagram method for systems of plane curves with base points
We develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne conjecture holds for systems with base points of equal multiplicity bounded by 42.
Cycles de Hodge absolus et périodes des intégrales des variétés abéliennes. (Rédigé par J. L. Brylinski)
Cycles évanescents et faisceaux pervers : cas des courbes planes irréductibles
Cyclic coverings of an elliptic curve with two branch points and the gap sequences at the ramification points