Researcher · UFRO
Ángel Carocca
Full Professor
Department of Mathematics and Statistics · Universidad de La Frontera
Biography
He obtained his Ph.D. in Mathematics from the Universidade de Brasília, Brazil, in 1992. He is currently a Full Professor in the Department of Mathematics and Statistics at Universidad de La Frontera. His research interests focus on group theory, Riemann surfaces, abelian varieties and group actions on these objects, in the context of Algebra and Geometry.
Research Areas
Group Theory
Group actions on Riemann surfaces
Abelian Varieties
Publications
On group actions on Riemann-Roch spaces of curves
J. Pure Appl. Algebra 228 (2024), no. 2, Paper No. 107451, 12 pp.
Abelian varieties and Riemann surfaces with generalized quaternion group action
J. Pure Appl. Algebra 227 (2023), no. 11, Paper No. 107398, 26 pp.
Decomposable Jacobians
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 4, 1673–1690.
Symmetric group actions on Jacobian varieties
Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces, Contemp. Math., 629, Amer. Math. Soc., 43–57.
Orbifolds with signature (0; k, kn−1, kn, kn)
Pacific J. Math. 263 (2013), no. 1, 53–85.
Jacobians with complex multiplication
Trans. Amer. Math. Soc. 363 (2011), no. 12, 6159–6175.
Prym and Prym-Tyurin varieties: a group-theoretical construction
In the tradition of Ahlfors-Bers. V, Contemp. Math., 510, Amer. Math. Soc., 49–60.
Prym-Tyurin varieties via Hecke algebras
J. Reine Angew. Math. 634 (2009), 209–234.
Prym-Tyurin varieties using self-products of groups
J. Algebra 322 (2009), no. 4, 1251–1272.
The quasi-superfluous elements of a group
JP J. Algebra Number Theory Appl. 13 (2009), no. 1, 99–107.
Products of Jacobians as Prym-Tyurin varieties
Geom. Dedicata 139 (2009), 219–231.
Generalized Humbert curves
Israel J. Math. 164 (2008), 165–192.
Jacobians with group actions and rational idempotents
J. Algebra 306 (2006), no. 2, 322–343.
Weyl groups and abelian varieties
J. Group Theory 9 (2006), no. 2, 265–282.
Criteria for the solubility and non-simplicity of finite groups
J. Algebra 285 (2005), no. 1, 58–72.
Dihedral groups acting on Jacobians
Complex manifolds and hyperbolic geometry, Contemp. Math., 311, Amer. Math. Soc., 41–77.
A note on solvability of factorizable finite groups
Hokkaido Math. J. 31 (2002), no. 2, 343–348.
Solvability of factorized finite groups
Glasg. Math. J. 42 (2000), no. 2, 271–274.
Theorems of Kegel-Wielandt type
Groups St. Andrews 1997 in Bath, I, London Math. Soc. Lecture Note Ser., 260, Cambridge Univ. Press, 195–201.
On a possible nonsimplicity criterion for finite factorized groups
Mat. Contemp. 14 (1998), 13–19.
Hypercentral embedding and pronormality
Arch. Math. (Basel) 71 (1998), no. 6, 433–436.
On factorized finite groups in which certain subgroups of the factors permute
Arch. Math. (Basel) 71 (1998), no. 4, 257–261.
Some solvability criteria for finite groups
Hokkaido Math. J. 26 (1997), no. 1, 157–161.
A note on the product of ℱ-subgroups in a finite group
Proc. Edinburgh Math. Soc. (2) 39 (1996), no. 1, 37–42.
A note on a theorem of W. Gaschütz and N. Itô
Bol. Soc. Brasil. Mat. (N.S.) 26 (1995), no. 2, 161–165.
Completeness properties of certain formations
Mat. Contemp. 6 (1994), 1–6.
The p-Huppert-subgroup and the set of p-quasi-superfluous elements in a finite group
Proc. Edinburgh Math. Soc. (2) 36 (1993), no. 2, 289–297.
p-supersolvability of factorized finite groups
Hokkaido Math. J. 21 (1992), no. 3, 395–403.
Research Grants
FONDECYT Regular · 1240181
On Group actions on Surfaces and Varieties, and their linear representations on related geometric objects
FONDECYT Regular · 1200608
On group representations and their actions on surfaces and varieties
MATH-AmSud · Código: MATH 2020014
Algebraic and geometric aspects of varieties and manifolds
REDES · Código: 190140
South-North Latin American network through Geometry
ECOS-Sud · Código: ECOS 190030
Geometry of K3 surfaces
MEC · Código: PAI80150021
Geometría de Grupos y Algebras (Invitado: Prof. Irina Markina, University of Bergen, Noruega)
FAPERJ–UFRO · Código: FPJ15-0001
La geometría de variedades complejas
FONDECYT Regular · 1130445
Group actions on complex Tori
Outreach and Extension
Community Outreach Project
Murales y voces que inspiran: Mujer y Ciencia
Graduate Supervision
Current Students
Vicente Chicaiza (Advisor)
Ph.D. in Mathematical Sciences · Universidad de La Frontera, Temuco, Chile
Thesis: Automorfismos y endomorfismos de variedades abelianas
Víctor Valdebenito (Co-advisor)
Doctorado en Ciencias mención Matemática · Universidad de La Frontera, Temuco, Chile
Graduated Students
Jaime Pinto (Advisor)
Ph.D. in Mathematical Sciences · Universidad de Chile, Santiago, Chile
Thesis: Curvas de tipo Fermat
Martha Romero (Advisor)
Ph.D. in Mathematics · Pontificia Universidad Católica de Chile, Santiago, Chile
Thesis: Grupo de monodromía de cubrimientos factorizados de superficies de Riemann
Daniela Vásquez (Advisor)
Ph.D. in Mathematical Sciences · Universidad de Chile, Santiago, Chile
Thesis: Acciones de grupos sobre el espacio de Riemann–Roch