Historical note

In the early seventies a generation of enthusiastic young people went into science in Chile. They were determined to continue graduate studies abroad and afterwards return to Chile to promote drastic changes in a broad spectrum of intellectual aspects of the national life.

C. H. Clemens was an US mathematician who helped many Chileans become mathematicians, and promoted the creation of a Complex Geometry Group in Chile. He encouraged Gonzalo Riera and Rubí Rodríguez in undertaking graduate studies at the Columbia University under the supervision of L. Bers. On the other hand, Víctor González ­Aguilera studied in Paris 7 under the supervision of J. L. Verdier and F. Norguet.

At the beginning of the eighties they returned to Chile and run a seminar in Santiago on the following subjects: Algebraic Geometry, Kleinian groups and Riemann surfaces. Their work during this period has been collected into yearly monographs.

The seminar attracted soon students and colleagues throughout the country, many of whom started to develop an interest in research, which was very little developed in the country at that time. As a consequence of their seminal work some chilean students got a master degree in Geometry under the supervision of the members of the Complex Geometry Group and several of these students went abroad to pursue their doctorate, after which they went back to join the group. The international collaborations, developed by the founders of the Complex Geometry Group, helped the Chilean mathematical community to exit from isolation and opened the way to the creation of PhD programs in Chile in the area of Geometry, favouring the attraction of foreign geometers. 

In 1998 a series of conferences named "Iberoamerican Congress on Geometry" were initiated in Chile, with the strong support of Irwin Kra (USA), Sevin Recillas (Mexico) and José María Muñoz Porras (Spain). The conferences took place every four years according to the following schedule:
  • Chile, 1998
  • Mexico, 2001
  • Spain, 2004
  • Brazil, 2007
  • Chile, 2010
  • New York, 2014
This is how the Chilean Group on Complex Geometry was formed and how it continues to grow.

The following (partial) list contains the people formed by Rubí, Víctor and Gonzalo:

  • Master students:

    • Silvia Vidal
    • Ximena Catepillán
    • Claudio del Pino
    • Juanita Contreras
    • Marcela Ilabaca
    • María Cecilia Tapia
    • Rubén Hidalgo (1987)
    • Alberto Castro (1986)
    • Jorge Bozo (1988)
    • Giancarlo Urzúa (2003)
    • Alvaro Liendo (2005)
    • Pedro Montero (2013)
  • Ph. D. students:

    • Gustavo Labbé (1995)
    • Anita Rojas (2002)
    • Carolina Becerra (2004)
    • Mariela Carvacho (2010)
    • Martha Romero (2013)
    • Robert Auffarth (2014)

Monographs, volumes and books:

  1. Seminario Geometría Compleja I
    U. Santa María, U. Santiago. Un seminario dirigido por Victor González y Rubí Rodrguez. Con la colaboración de Claudio Troncoso, Luis Salinas, Sergio Plaza, Cecilia Tapia, Bernardo León de la Barra. 1983

  2. Seminario Geometría Compleja I 1/2
    U. Santa María, U. Santiago. Actas primer encuentro nacional de Geometría Compleja. Un seminario dirigido por Victor González y Rubí Rodríguez. 1984

  3. Complex Geometry Seminar, volume II
    Universidad Técnica Federico Santa María. Edited by Victor González A. and Rubí Rodríguez M, with the collaboration of Gonzalo Riera L. 1986

  4. Complex Geometry Seminar, volume III
    P. Universidad Católica de Chile y Universidad Técnica Federico Santa María. Edited by Victor González A. and Rubí Rodríguez M, with the collaboration of Gonzalo Riera L. and Rubén Hidalgo O. 1994

  5. Taller de Variedades Abelianas y Funciones Theta
    Aportaciones Matemáticas: Investigación 13, Sociedad Matemática Mexicana, 1998. Papers from the International Workshop held in Morelia, July 8­­27, 1996 Rubí E. Rodríguez, José María Muñoz Porras and Sevín Recillas

  6. Complex Geometry of Groups
    Contemporary Mathematics 240, American Mathematical Society, 1999.  Proceedings of the 1st Iberoamerican Cruz del Sur Congress on Geometry held in Olmué, Chile, January 5­1, 1998. A. Carocca, V. González ­Aguilera, Rubí E. Rodríguez.

  7. Imaginando Isometrías
    Víctor H. Cortés and Rubí E. Rodríguez Ministry of Education, Chile, First edition 1999 and Second edition 2002.

  8. The geometry of Riemann surfaces and abelian varieties
    Contemporary Mathematics 397, American Mathematical Society, 2006. Papers from the 3rd Iberoamerican Congress on Geometry in honor of Professor Sevín Recillas­ Pishmish's 60 2004 José M. Muñoz Porras, Sorin Popescu and Rubí E. Rodríguez.

  9. Complex analysis. In the spirit of Lipman Bers
    Second edition. Rodríguez, Rubí E.; Kra, Irwin; Gilman, Jane P. Graduate Texts in Mathematics, 245. Springer, New York, 2013

Selected publications:

  • Carocca, Angel; Hidalgo, Rubén A.; Rodríguez, Rubí E. Orbifolds with signature (0;k,kn−1,kn,kn). Pacific J. Math. 263 (2013), no. 1, 53–85.

  • González ­Aguilera, V.; Munoz­Porras, J. M.; Zamora, A. G. On the irreducible components of the singular locus of Ag. II. Proc. Amer. Math. Soc. 140 (2012), no. 2, 479–492.

  • Gómez González, Esteban; Muñoz Porras, José M.; Plaza Martín, Francisco J.; Rodríguez, Rubí E. Characterizations of Jacobians of curves with automorphisms. Trans. Amer. Math. Soc. 362 (2010), no. 10, 5373–5394.

  • González ­Aguilera, Víctor On a Schottky problem for the singular locus of A5. Geometry of Riemann surfaces, 217–237, London Math. Soc. Lecture Note Ser., 368, Cambridge Univ. Press, Cambridge, 2010.

  • Carocca, Angel; Lange, Herbert; Rodríguez, Rubí E.; Rojas, Anita M. Prym­Tyurin varieties via Hecke algebras. J. Reine Angew. Math.634 (2009), 209–234.

  • Costa, Antonio F.; Izquierdo, Milagros; Riera, Gonzalo One­dimensional Hurwitz spaces, modular curves, and real forms of Belyi meromorphic functions. Int. J. Math. Math. Sci. 2008, Art. ID 609425, 18 pp.

  • Carocca, Angel; González­Aguilera, Víctor; Rodríguez, Rubí E. Weyl groups and abelian varieties. J. Group Theory 9 (2006), no. 2, 265–282. the birthday held at the University of Salamanca, Salamanca, Spain, June 8­­12,

  • Riera, Gonzalo A formula for the Weil­Petersson product of quadratic differentials. J. Anal. Math. 95 (2005), 105–120.

  • Costa, Antonio F.; Riera, Gonzalo One parameter families of Riemann surfaces of genus two. Glasg. Math. J. 43 (2001), no. 2, 255–268.

  • Bujalance, E.; Costa, A. F.; Gamboa, J. M.; Riera, G. Period matrices of Accola­Maclachlan and Kulkarni surfaces. Ann. Acad. Sci. Fenn. Math. 25 (2000), no. 1, 161–177.

  • González­Aguilera, Víctor; Rodríguez, Rubí E. Families of irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves. Proc. Amer. Math. Soc. 128 (2000), no. 3, 629–636.

  • Riera, Gonzalo; Rodríguez, Rubí E. Riemann surfaces and abelian varieties with an automorphism of prime order. Duke Math. J. 69(1993), no. 1, 199–217.

  • Riera, Gonzalo; Rodríguez, Rubí E. The period matrix of Bring's curve. Pacific J. Math. 154 (1992), no. 1, 179–200.

  • Riera, Gonzalo; Rodríguez, Rubí Uniformization of surfaces of genus two with automorphisms. Math. Ann. 282 (1988), no. 1, 51–67.