Personal webpage of Robert Auffarth

I am the assistant dean of the Faculty of Science of the University Chile, as well as associate professor of the Mathematics Department of the Faculty of Science of the University of Chile.

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.

Publications

On the Picard number and the extension degree of period matrices of complex tori. To appear in Journal of Pure and Applied Algebra. arXiv:2503.21642. Joint work with Jorge Duque.
A note on multisecants of the Kummer variety of Jacobians. To appear in Archiv der Mathematik, 2025. arXiv:2502.07197. Joint work with Sebastián Rahausen.
Pseudoinversos de morfismos entre variedades abelianas. Accepted in CUBO, special Spanish edition, 2025.
On the Jacobian variety of the Accola-Maclachlan curve of genus four. Accepted in New Tools in Mathematical Analysis and Applications - Proceedings of the 14th ISAAC Congress 2023, Ribeirão Preto, Brazil. Joint work with Sebastián Reyes Carocca and Anita Rojas.
Non-simple polarised abelian surfaces and genus 3 curves with completely decomposable Jacobians. Annali di Matematica (accepted 2024). https://doi.org/10.1007/s10231-023-01415-x. Joint work with Pawel Borowka.
Smooth quotients of abelian surfaces by finite groups that fix the origin. CUBO 24 (2022), 37--51. Joint work with Giancarlo Lucchini Arteche and Pablo Quezada.
Smooth quotients of complex tori by finite groups. Math. Z. 300 (2022), 1071--1091 Joint work with Giancarlo Lucchini Arteche, appendix by Stephen Griffeth.
Smooth quotients of principally polarized abelian varieties. Mosc. Math. J. 22 (2022), 225--237. Joint work with Giancarlo Lucchini Arteche.
Galois subspaces for the rational normal curve. Commun. Algebra 49 (2021), 3635--3644. Joint work with Sebastián Rahausen.
Galois subspaces for smooth projective curves. J. Algebra 572 (2021), 146--162. Joint work with Sebastián Rahausen.
A decomposition of the Jacobian of a Humbert-Edge curve. In ``Geometry at the Frontier: Symmetries and Moduli Spaces of Algebraic Varieties'', Contemp. Math. 766 (2021), 31--38. Joint work with Giancarlo Lucchini Arteche and Anita Rojas.
Smooth quotients of abelian varieties by finite groups. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XXI (2020), 673--694. 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.
On a numerical characterization of non-simple principally polarized abelian varieties. Math. Z. 282 (2016), no. 3--4, 731--746.
Elliptic curves on abelian varieties. Illinois J. Math. 59, no. 2 (2015), 319--336.

Preprints

Pseudoreflections on Prym varieties. Preprint, 2024. arXiv:2412.04940. Joint work with Martí Lahoz and Juan Carlos Naranjo.
Counting principal polarizations on abelian varieties with automorphisms. Preprint, 2024. arXiv:2412.01676. Joint work with Angel Carocca and Rubí E. Rodríguez.
Galois subspaces for projective varieties. Preprint, 2023. arXiv:2306.04051.

Current students

Génesis Cornejo, Group laws on rational curves. Masters in Mathematics. Expected defense date: December 2025.
Ignacio Ibarra, The Grothendieck group of complex tori. Masters in Mathematics. Expected defense date: January 2026.

Former students

Sebastián Rosselot. Galois subspaces for products of elliptic curves. Masters in Mathematics. Defense date: October 22, 2025.
Sebastián Rahausen. The generalized Torelli problem through the geometry of the Gauss map. Ph.D. in Mathematics, P. Universidad Católica de Chile. Defense date: June 25, 2024.
Camila Muñoz Santander. On abelian subvarieties of bounded degree on an abelian variety. Ph.D. in Mathematics, Universidad de Chile. Defense date: June 5, 2024.
José Aburto. Secants to the Kummer variety. Ph.D. in Mathematics, Universidad de Chile. Defense date: January 12, 2023.
Nelson Alvarado. Toroidal compactifications of polarized abelian varieties. Masters in Mathematics. Universidad de Chile. Defense date: August 23, 2021.
Gary Martínez. Fibrations associated to smooth quotients of abelian varieties. Masters in Mathematics, Universidad de Chile. Coadvisor along with Giancarlo Lucchini Arteche. Defense date: March 9, 2021.
Sebastián Rahausen. Galois subspaces for the rational normal curve. Masters in Mathematics, Universidad de Chile. Defense date: January 30, 2019.
Pablo Quezada. Smooth quotients of abelian surfaces by finite groups. Masters in Mathematics, P. Universidad Católica de Chile. Coadvisor along with Giancarlo Lucchini Arteche. Defense date: January 22, 2019.
Matías Alvarado. Fixed points of endomorphisms of complex tori. Masters in Mathematics, Universidad de Chile. Defense date: March 11, 2018.

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