Contemporary Mathematics 1999; 286 pp; softcover Volume: 240 ISBN10: 0821813811 ISBN13: 9780821813812 List Price: US$84 Member Price: US$67.20 Order Code: CONM/240
 This volume presents the proceedings of the I Iberoamerican Congress on Geometry: Cruz del Sur held in Olmué, Chile. The main topic was "The Geometry of Groups: Curves, Abelian Varieties, Theoretical and Computational Aspects". Participants came from all over the world. The volume gathers the expanded contributions from most of the participants in the Congress. Articles reflect the topic in its diversity and unity, and in particular, the work done on the subject by Iberoamerican mathematicians. Original results and surveys are included on the following areas: curves and Riemann surfaces, abelian varieties, and complex dynamics. The approaches are varied, including Kleinian groups, quasiconformal mappings and Teichmüller spaces, function theory, moduli spaces, automorphism groups, algebraic geometry, and more. Readership Graduate students and research mathematicians interested in functions of a complex variable. Table of Contents  R. E. Rodríguez  Complex geometry in Chile: Panorama and perspectives
 W. Abikoff  Quasiconformal conjugation of Möbius transformations
 R. Bamón  A family of ndimensional differential equations with Lorenzlike attractors
 C. Birkenhake, H. Lange, and V. GonzálezAguilera  Automorphisms of \(3\)dimensional abelian varieties
 L. BrambilaPaz, L. HidalgoSolís, and J. MuciñoRaymundo  On restrictions of the Picard bundle
 A. M. Castro  Representations of triangle groups in the Heisenberg group
 M. Chuaqui and B. Osgood  Recent progress on the geometry of univalence criteria
 A. F. Costa and A. M. Porto  On anticonformal automorphisms of order \(>2\) of Riemann
 C. J. Earle, F. P. Gardiner, and N. Lakic  Isomorphisms between generalized Teichmüller spaces
 H. M. Farkas and I. Kra  Ramanujan partition identities
 H. M. Farkas and I. Kra  A function theoretic approach to the Ramanujan partition identities with applications to combinatorial number theory
 F. Gardiner and L. Keen  Holomorphic motions and quasifuchsian manifolds
 L. Giraldo, X. GómezMont, and P. Mardešić  Computation of topological numbers via linear algebra: hypersurfaces, vector fields and vector fields on hypersurfaces
 E. Gómez González  Cyclic coverings of a smooth curve and branch locus of the moduli space of smooth curves
 G. GonzálezDíez and W. J. Harvey  Subvarieties of moduli space for Riemann surfaces
 R. A. Hidalgo  Noded function groups
 L. HidalgoSolís and S. RecillasPishmish  The hyperelliptic fibre of the Prym map in genus four
 J. Kiwi  From the shift loci to the connectedness loci of complex polynomials
 Y. A. Kopylov  Some properties of the operator of exterior derivation on surfaces of revolution and \(\mathbb{L_p}\)cohomology
 B. Maskit  Matrices for FenchelNielsen parameters in genus \(2\)
 T. Nakanishi, M. Näätänen, and G. Rosenberger  Arithmetic Fuchsian groups of signature \((0;e_1,e_2,e_3,e_4)\) with \(2 \leq e_1 \leq e_2 \leq e_3\), \(e_4 = \infty\)
 J. R. Quine  Geometric and holomorphic moduli for extremal Riemann surfaces
