Criteria for complex multiplication and transcendence properties of automorphic functions.
Criteria for Quasi-Projectivity.
Critical and ramification points of the modular parametrization of an elliptic curve
Let be an elliptic curve defined over with conductor and denote by the modular parametrization:In this paper, we are concerned with the critical and ramification points of . In particular, we explain how we can obtain a more or less experimental study of these points.
Critical Points of an Algebraic Function.
Crystalline boundedness principle
Crystalline conjecture via -theory
Crystalline Dieudonné module theory via formal and rigid geometry
Crystalline Dieudonné theory over excellent schemes
Cubic differential forms and the group law on the Jacobian of a real algebraic curve
In an earlier paper [6], we gave an explicit geometric description of the group law on the neutral component of the set of real points of the Jacobian of a smooth quartic curve. Here, we generalize this description to curves of higher genus. We get a description of the group law on the neutral component of the set of real points of the Jacobian of a smooth curve in terms of cubic differential forms. When applied to canonical curves, one gets an explicit geometric description of this group law by...
Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces
Cubic structures and ideal class groups
Cubic surfaces with a Galois invariant double-six
We present a method to construct non-singular cubic surfaces over ℚ with a Galois invariant double-six. We start with cubic surfaces in the hexahedral form of L. Cremona and Th. Reye. For these, we develop an explicit version of Galois descent.
Cubic theta relations.
Curvature on holomorphic plane curves. II
Curves and their fundamental groups
Curves in P² and symplectic packings.
Curves in P2(C) with 1-dimensional symmetry.
In a previous paper we showed that the existence of a 1-parameter symmetry group of a hypersurface X in projective space was equivalent to failure of versality of a certain unfolding. Here we study in detail (reduced) plane curves of degree d ≥ 3, excluding the trivial case of cones. We enumerate all possible group actions -these have to be either semisimple or unipotent- for any degree d. A 2-parameter group can only occur if d = 3. Explicit lists of singularities of the corresponding curves are...
Curves of
Curves of genus 2 and Desargues configurations.
Curves of genus 2, continued fractions, and Somos sequences.