Rubí E. Rodríguez

The Geometry of Riemann Surfaces and Abelian Varieties

Mobius transformations of the circle form a maximal convergence group by A. Basmajian and M. Zeinalian On the polar linear system of a foliation by curves in a projective space by A. Campillo and J. Olivares Birational classification of hyperelliptic real algebraic curves by F. J. Cirre The genus two Jacobians that are isomorphic to a product of elliptic curves by C. J. Earle Vanishing thetanulls and Jacobians by H. M. Farkas Theta functions, geometric quantization and unitary Schottky bundles by C. Florentino, J. Mourao, and J. P. Nunes Smooth double coverings of hyperelliptic curves by Y. Fuertes and G. Gonzalez-Diez Planar families of discrete groups by J. Gilman and L. Keen Generalized addition formulae for theta functions by E. Gomez Gonzalez and C. Gonzalez-Martinez Curves with a group action and Galois covers via infinite Grassmannians by E. Gomez Gonzalez and F. J. P. Martin Some recent results on the irreducible components of the singular locus of

Families of irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves

A_g

A pencil in Open image in new window with three points at the boundary

by V. Gonzalez-Aguilera, J. M. Munoz-Porras, and A. G. Zamora A note on the arithmetic genus of reducible plane curves by M. R. Gonzalez-Dorrego Teichmuller curves defined by characteristic origamis by F. Herrlich Lowest uniformizations of compact real surfaces by R. A. Hidalgo and B. Maskit Principal polarizations on products of elliptic curves by H. Lange An approach to a 2-dimensional Contou-Carrere symbol by F. P. Romo Prym varieties and fourfold covers II: The dihedral case by S. Recillas and R. E. Rodriguez Examples for Veech groups of origamis by G. Schmithusen Genus 2 translation surfaces with an order 4 automorphism by R. Silhol The Pfaffian structure defining a Prym theta divisor by R. Smith and R. Varley.

Jacobians with complex multiplication

For each n greater than or equal to two, we give a family of n–dimensional, irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves. This family corresponds to the modular curve X0(n + 1).

Prym-Tyurin varieties via Hecke algebras

AbstractWe construct a linear pencilCt of curves in, such that for eacht ∈ ℙ1, Aut(Ct) contains the alternating group

A generalisation of Kani-Rosen decomposition theorem for Jacobian varieties

\mathfrak{U}_5

The Fundamental Theorem in Complex Function Theory

and we describe the curves of the pencil contained on the boundary of.We construct a linear pencilCt of curves in Open image in new window , such that for eacht ∈ ℙ1, Aut(Ct) contains the alternating group\(\mathfrak{U}_5 \) and we describe the curves of the pencil contained on the boundary of Open image in new window .

The Cauchy Theory: Key Consequences

We construct and study two series of curves whose Jacobians admit complex multiplication. The curves arise as quotients of Galois coverings of the projective line with Galois group metacyclic groups