On real algebraic vector bundles.
On the number of connected components of real abelian varieties that admit sufficiently many compley multiplications.
The underlying real algebraic structure of complex elliptic curves.
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...
Strict uniformization of real algebraic curves and global real analytic coordinates on real Teichmüller spaces.
We construct a global system of real analytic coordinates on the real Teichmüller space of a compact real algebraic curve X, using so-called strict uniformization of the real algebraic curve X. A global coordinate system is then obtained via real quasiconformal deformations of the Kleinian subgroup of PGL2(R) obtained as a group of covering transformations of a strict uniformization of X.
On the geometry of algebraic curves having many real components.
We show that there is a large class of nonspecial effective divisors of relatively small degree on real algebraic curves having many real components i.e. on M-curves. We apply to 1. complete linear systems on M-curves containing divisors with entirely real support, and 2. morphisms of M-curves into P1.
When is a complex elliptic curve the product of two real algebraic curves?
Page 1