Anita M. Rojas
Departamento de Matemáticas
Facultad de Ciencias
Universidad de Chile
E-mail: anirojas at uchile dot cl
Phone: (+56) 2 2978 7311
Address: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, 7800024 Ñuñoa, Santiago, Chile.
Research topics
Algebraic curves, Abelian varieties, their moduli spaces and the locus of objects with group actions or other special properties (complex multiplication, Prym-Tyurin varieties of low exponent, etc.) Currently I am involved in learning about special and Shimura varieties.
Recent publications
Hidalgo, Rubén, Paulhus, Jennifer, Reyes-Carocca, Sebastián; Rojas, Anita M.; On Non-Normal Subvarieties of the Moduli Space of Riemann Surfaces. Transformation Groups (to appear). https://doi.org/10.1007/s00031-024-09870-3
Rodríguez, Rubí E.; Rojas, Anita M.; A Fruitful Interaction Between Algebra, Geometry, and Topology: Varieties Through the Lens of Group Actions. Notices Amer. Math. Soc. 71 (2024), no.6, 715–723. https://doi.org/10.1090/noti2950 or On-line version
Behn, Antonio; Rojas, Anita M.; Tello-Carrera, Miguel; A SAGE Package for n-Gonal Equisymmetric Stratification of Mg. Exp. Math. 32 (2023), no. 1, 54–69. https://doi.org/10.1080/10586458.2020.1763872
Reyes-Carocca, Sebastián; Rojas, Anita M. On large prime actions on Riemann surfaces. J. Group Theory 25 (2022), no. 5, 887–940. https://doi.org/10.1515/jgth-2020-0140
Auffarth, Robert; Lucchini Arteche, Giancarlo; Rojas, Anita M. A decomposition of the Jacobian of a Humbert-Edge curve. Geometry at the frontier—symmetries and moduli spaces of algebraic varieties, 31–38, Contemp. Math., 766, Amer. Math. Soc. Electronic ISBN: 978-1-4704-6422-6. http://dx.doi.org/10.1090/conm/766/15371
Izquierdo, Milagros; Reyes-Carocca, Sebastián; Rojas, Anita M. On families of Riemann surfaces with automorphisms. J. Pure Appl. Algebra 225 (2021), no. 10, Paper No. 106704, 21 pp. https://doi.org/10.1016/j.jpaa.2021.106704.
Other reports
Carolina Becerra-Osses and Anita M. Rojas . Uso experimental de Kahoot! y Socrative en Docencia Universitaria. Poster at the Congreso de las Américas sobre Educación Internacional (CAEI), October 19 - 22, 2021.
Anita M. Rojas (2020): Campamento MateA: Matemáticas para alumnas y profesores de enseñanza media. En Póo Figueroa, X., Dougnac Quintana, P., Flores González, M., Osorio Arredondo, F., Ravanal Ponce, M. y Sánchez Riadi, A. (2020). Extensión con sentido país: innovando en las prácticas de extensión, vinculación con el medio y comunicaciones en la Universidad de Chile 2016-2018 . Available in (Spanish) http://libros.uchile.cl/1106, pp. 299-307.
Dissemination posts
Anita M. Rojas (2024): Ciento cincuenta años de trascendencia, celebrando el mes de la Matemática. In El mostrador, cultura.
Less recent publications
Izquierdo, Milagros; Jiménez, Leslie; Rojas, Anita Decomposition of Jacobian varieties of curves with dihedral actions via equisymmetric stratification. Rev. Mat. Iberoam. 35 (2019), no. 4, 1259–1279.(DOI: 10.4171/rmi/1084).
Paulhus, Jennifer; Rojas, Anita M. Completely decomposable Jacobian varieties in new genera. Exp. Math. 26 (2017), no. 4, 430–445.
Auffarth, R.; Lange, H.; Rojas, A. M. A criterion for an abelian variety to be non-simple. J. Pure Appl. Algebra 221 (2017), no. 8, 1906–1925.
Barraza, Patricio; Rojas, Anita M. The group algebra decomposition of Fermat curves of prime degree. Arch. Math. (Basel) 104 (2015), no. 2, 145–155.
Carocca, Angel; Rodríguez, Rubí E.; Rojas, Anita M. Symmetric group actions on Jacobian varieties. Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces, 43–57, Contemp. Math., 629, Amer. Math. Soc., Providence, RI, 2014.
Lange, Herbert; Rodríguez, Rubí E.; Rojas, Anita M. Polarizations on abelian subvarieties of principally polarized abelian varieties with dihedral group actions. Math. Z. 276 (2014), no. 1-2, 397–420.
Behn, Antonio; Rodríguez, Rubí E.; Rojas, Anita M. Adapted hyperbolic polygons and symplectic representations for group actions on Riemann surfaces. J. Pure Appl. Algebra 217 (2013), no. 3, 409–426.
Lange, Herbert; Rojas, Anita M. Polarizations of isotypical components of Jacobians with group action. Arch. Math. (Basel) 98 (2012), no. 6, 513–526.
Carocca, Angel; Lange, Herbert; Rodríguez, Rubí E.; Rojas, Anita M. Prym and Prym-Tyurin varieties: a group-theoretical construction. In the tradition of Ahlfors-Bers. V, 49–60, Contemp. Math., 510, Amer. Math. Soc., Providence, RI, 2010.
Arenas-Carmona, Luis; Rojas, Anita M. Unramified prime covers of hyperelliptic curves and pairs of p-gonal curves. In the tradition of Ahlfors-Bers. V, 35–47, Contemp. Math., 510, Amer. Math. Soc., Providence, RI, 2010.
Carocca, Angel; Lange, Herbert; Rodríguez, Rubí E.; Rojas, Anita M. Prym-Tyurin varieties via Hecke algebras. J. Reine Angew. Math. 634 (2009), 209–234.
Carocca, Angel; Lange, Herbert; Rodríguez, Rubí E.; Rojas, Anita M. Prym-Tyurin varieties using self-products of groups. J. Algebra 322 (2009), no. 4, 1251–1272.
Carocca, Angel; Lange, Herbert; Rodríguez, Rubí E.; Rojas, Anita M. Products of Jacobians as Prym-Tyurin varieties. Geom. Dedicata 139 (2009), 219–231.
Lange, Herbert; Rojas, Anita M. A Galois-theoretic approach to Kanev's correspondence. Manuscripta Math. 125 (2008), no. 2, 225–240.
Rojas, Anita M. Group actions on Jacobian varieties. Rev. Mat. Iberoam. 23 (2007), no. 2, 397–420.
Lange, H.; Recillas, S.; Rojas, A. M. A family of Prym-Tyurin varieties of exponent 3. J. Algebra 289 (2005), no. 2, 594–613.
Plarre, K.; Rojas, A. M.; Rojas, R. A. Analytical solution to the polynomial diophantine equation: development and application to Generalised Predictive Control analysis, IEE CONFERENCE PUBLICATIONS 455-1, 804-809. doi.org/10.1049/cp:19980332.
Recent grants
Research grants
FONDECYT REGULAR 1230034: Subvarieties and loci in moduli spaces, April 2023 - March 2027.
Math AmSud grant GV-BCEF: The geometry of varieties. Group actions, symmetries, moduli and beyond. (Website)
FONDECYT REGULAR 1180073: Riemann surfaces, abelian varieties and their moduli spaces, May 2018 - March 2023.
CONICYT PIA 1415: "Geometry at the Frontier". Its mission is to contribute to the development of Complex Geometry and its applications
Grants for innovation in teaching
Fondo de Incentivo a la Investigación en Docencia de Pregrado, Vicerrectoría de Asuntos Académicos, Universidad de Chile. "Diseño de experimentos matemáticos como parte de la reflexión de la práctica docente para contribuir a una mejora en la trayectoria formativa de estudiantes en cursos de matemáticas (FIDOP 2023_02_FCS)." August 2023 to December 2024. Website selected projects FIDOP 2023
Fondo de incentivo a la innovación en docencia mediada por tecnología, Vicerrectoría de Asuntos Académicos, Universidad de Chile. Awarded in June de 2024. "Implementación de Experimentos Matemáticos para contribuir a una mejora en la trayectoria formativa de estudiantes en cursos de matemáticas". Website of the calling
Collaborations
With Robert Auffarth, we have been studying the Néron-Severi group of an abelian variety, to describe the non-simplicity of it.
With Milagros Izquierdo and Sebastián Reyes-Carocca, we have been working on group actions on Riemann surfaces, equisymmetric stratification and moduli spaces of Riemann surfaces.
With Jennifer Paulhus and Giancarlo Lucchini Arteche we have been working on decomposable abelian varieties, in particular completely decomposable abelian varieties.
With Rubí E. Rodríguez, Angel Carocca and Herbert Lange, we have been working on abelian varieties with group actions, Prym-Tyurin varieties and moduli problems.
With Juliana Coelho, we have been thinking about how decompositions of Jacobian varieties reflect into their subvarieties; in particular, we are interested on Brill-Noether varieties.
Other IDs or references
Graduate students
Automorphisms and Weierstrass points on Riemann surfaces, by Rodrigo Contreras-Martínez, Magister en Ciencias Matemáticas, Universidad de Chile, April 2024. Available at https://repositorio.uchile.cl/handle/2250/198454
On the geometry of the action of finite linked groups: Isogenous Jacobian varieties via intermediate coverings, by Estefanía Bravo, Doctorado en Ciencias mención Matemáticas (PhD), Universidad de Chile, 2022. Available at https://repositorio.uchile.cl/handle/2250/185075
Equivalencia de Acciones de Grupos sobre Superficies de Riemann y Estratificación, by Miguel Ángel Tello-Carrera, Magister en Ciencias Matemáticas, Universidad de Chile, April 2019. Available at http://repositorio.uchile.cl/handle/2250/171536
Weyl group actions over Jacobian varieties, by Miguel Román. Magíster en Matemáticas, Pontificia Universidad Católica de Chile, 2016. ( Tutor, Co-tutor: Sukhendu Mehrotra). Available at https://www.mat.uc.cl/archivos/weyl-group-actions-on-jacobian-varieties.pdf
Curvas de tipo Fermat, by Jaime Pinto Doveris, Doctorado en Ciencias mención Matemáticas, Universidad de Chile, Agosto 2016. (Co-tutor, Tutor: Ángel Carocca). Available at https://repositorio.uchile.cl/handle/2250/192123
On the kernel of the Group algebra decomposition of a Jacobian variety, by Leslie Jiménez Palma, Doctorado en Ciencias mención Matemáticas, Universidad de Chile, Junio 2014. Available at https://repositorio.uchile.cl/handle/2250/192130
Clasificación topológica de acciones de grupos en Superficies de Riemann. Un método algebraico, by Camila Muñoz Santander, Magíster en Ciencias Matemáticas, Universidad de Chile, Mayo 2014. Available at https://repositorio.uchile.cl/handle/2250/188864
Acciones de Grupos sobre el espacio de Riemann-Roch, by Daniela Vásquez Latorre, Doctorado en Ciencias mención Matemáticas, Universidad de Chile, Diciembre 2013. (Co-tutor, Tutor: Ángel Carocca). Available at https://repositorio.uchile.cl/handle/2250/189148
Polígonos hiperbólicos y Representaciones simplécticas para acciones de grupos en Superficies de Riemann, aplicaciones a Variedades Abelianas, by Sandy Schumacher, Magíster en Ciencias Matemáticas, Universidad de Chile, 2012. Available at https://repositorio.uchile.cl/handle/2250/188880
Ecuaciones para Superficies de Riemann correspondientes a cubrimientos cíclicos primos, by Jaime Pinto, Magíster en Matemáticas, Universidad de Chile, 2012. Available at https://repositorio.uchile.cl/handle/2250/188904
Curvas de Fermat y descomposición de objetos (geométricos) asociados, Patricio Barraza, Magíster en Matemáticas, Pontificia Universidad Católica de Chile, 2009. Available at https://www.mat.uc.cl/archivos/dip/tesis-postgrado/magister-mat/tesis-patricio-barraza-vargas.pdf
Some conferences, seminars, schools, etc.
To come,
Speaker at the "Coloquio Latinoamericano de Teoría de Números", Red Latinoamericana de Teoría de Números (ReLATeN), Uruguay. April 24, 2025 (online). (Website)
Past,
Co-organizer of the "Jornada de Geometría en el Magister" (JGM-JGM), Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile. March 18, 2025. (Website).
Speaker at the minicourse "Complex abelian varieties", Universidad Federal Fluminense, Niteroi, Brasil. February 3-7, 2025. (Website).
Organizing committee at the CIMPA school on Serre's big image theorem for Galois representation associated to elliptic curves, Universidad de Valparaiso, Valparaiso, Chile. January 6-17, 2025. (Website).
Speaker at the XXXII del Congreso de Matemática Capricornio COMCA2024, Universidad de Tarapacá, Arica, July 31 to August 2, 2024.(Website)
Speaker at the XXIV Coloquio Latinoamericano de Álgebra, Pontificia Universidad Católica de Chile, Santiago. July 22-26, 2024. (Website).
Speaker at the MATH-AmSUD workshop on Algebraic Geometry, Laboratoire Dieudonné, Université Côte d'Azur, Nice, France. June 17-21, 2024. (Website).
Speaker at the Matematiska kollokviet, University of Linköping, Sweden. June 12, 2024. (Website).
Speaker at the Algebra Seminar, University of Linköping, Sweden. June 11, 2024. (Website).
Speaker at the meeting “Mujeres Geómetras desde la Línea Ecuatorial”, online event organized by the Grupo Geometría Ecuador-GGEc. May 10, 2024.
Co-organizer of the MATH-AmSud School on Geometry, December 4th to 7th 2023, El Quisco, Chile. (Website).
Co-organizer of the Special session "Matemáticas en Educación Superior" at the XCI Encuentro de la Sociedad de Matemática de Chile, December 18th to 21st 2023, Facultad de Ciencias, Universidad de Chile.
Co-organizer of the "Escuela de Geometría Primavera en las Palmeras", October 19-21, 2022, Facultad de Ciencias, Universidad de Chile.
Co-organizer of the MateA: Math camp for girls and teachers. Three on-site versions: January 3rd-6th 2017, January 3rd-5th 2018 and December 12th-14th 2018. Two online-asynchronic versions (January 2020, October 2021).
Co-organizer of the Conference to honour our founders: Rubí E. Rodriguez, Víctor González-Aguilera and Gonzalo Riera, Universidad de La Frontera, 9 - 12 December, 2014, Temuco, Chile.
Links
Escuela de Ciencias, Facultad de Ciencias, Universidad de Chile.
Coloquio Las Palmeras, our local Math Department seminar.
Departamento de Matemáticas , Facultad de ciencias, Universidad de Chile.
LMFDB: Families of Higher Genus Curves with Automorphisms Site with algorithms for group actions on Riemann surfaces and applications (by Jen Paulhus).
Group names database, Under construction at GroupNames.org
