Personal webpage of Robert Auffarth

I am an assistant professor at the Mathematics Department of the Facultad de Ciencias of the Universidad de Chile.

Teaching:

This semester I'm teaching the undergraduate course Grupos y Anillos, as well as the graduate course Variedades Abelianas.

My youtube channel with online classes can be found here.


Research interests:

Most of my work involves abelian varieties, curves and their Jacobians, and moduli spaces of these objects. I am also interested in Prym varieties, Prym-Tyurin varieties, secants of Kummer varieties of abelian varieties, and group actions on curves and abelian varieties.


Recent publications

  • A decomposition of the Jacobian of a Humbert-Edge curve. To appear in Contemporary Mathematics. Joint work with Giancarlo Lucchini Arteche and Anita Rojas.
  • Smooth quotients of abelian varieties by finite groups. To appear in Annali della Scuola Normale Superiore di Pisa. Joint work with Giancarlo Lucchini Arteche.
  • Theta divisors whose Gauss map has a fiber of positive dimension. J. Algebra 548 (2020), 153-161. Joint work with Giulio Codogni.
  • The Gauss map and secants of the Kummer variety. B. Lond. Math. Soc. 51 (2019), 489-500. Joint work with Giulio Codogni and Riccardo Salvati Manni.
  • Fixed points of endomorphisms of complex tori. J. Algebra 507 (2018), 428-438. Joint work with Matías Alvarado.
  • Direct image of parabolic line bundles. J. Pure. Appl. Algebra 222 (2018), no. 5, 1189-1202. Joint work with Indranil Biswas.
  • A note on Galois embeddings of abelian varieties. Manuscripta Math. 154 (2017), no. 3-4, 279-284.
  • Torsion points on theta divisors. Proc. of the Amer. Math. Soc. Volume 145, Number 1 (2017), 89-99. Joint work with Gian Pietro Pirola and Riccardo Salvati Manni.
  • A criterion for an abelian variety to be non-simple. J. Pure Appl. Algebra. Volume 221, Number 8 (2017), 1906-1925. Joint work with Herbert Lange and Anita Rojas.


Preprints

  • Galois subspaces for smooth projective curves. Joint work with Sebastián Rahausen.
  • Smooth quotients of abelian varieties by finite groups II (with an appendix by Stephen Griffeth). arXiv:1912.05327. Joint work with Giancarlo Lucchini Arteche.
  • Smooth quotients of principally polarized abelian varieties. arXiv:1901.07049. Joint work with Giancarlo Lucchini Arteche.
  • Smooth quotients of abelian surfaces by finite groups. arXiv:1809.05405. Joint work with Giancarlo Lucchini Arteche and Pablo Quezada.
  • Galois embeddings of the projective line. arXiv:1809.02635. Joint work with Sebastián Rahausen.


Students

  • Sebastián Rahausen. Masters student. "Subespacios de Galois para la curva racional normal". Defense date: January 30, 2019.
  • Pablo Quezada. Masters student. "Cocientes suaves de superficies abelianas por grupos finitos". Defense date: January 22, 2019.
  • Matías Alvarado. "Puntos fijos de endomorfismos de toros complejos". Defense date: March 11, 2018.
  • Camila Muñoz. Current Ph.D. student.
  • José Aburto. Current Ph.D. student.
  • Gary Martínez. Current Masters student.
  • Nelson Alvarado. Current Masters student.


Collaborators

  • Indranil Biswas
  • Giulio Codogni
  • Herbert Lange
  • Giancarlo Lucchini Arteche
  • Gian Pietro Pirola
  • Anita Rojas
  • Riccardo Salvati Manni