Ángel Carocca — Geometry at the Frontier · UFRO

Researcher · UFRO

Ángel Carocca

Full Professor

Department of Mathematics and Statistics · Universidad de La Frontera

Ph.D. in Mathematics, University of Brasilia, Brazil (1992)
B.Sc. in Mathematics, Pontificia Universidad Católica de Valparaíso, Chile (1987)
+56 45 232 53 44
Office 222
Ángel Carocca
01
About the researcher

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.

02
 

Research Areas

Group Theory

Group actions on Riemann surfaces

Abelian Varieties

03
Scientific output · 36 indexed articles

Publications

36 of 36 articles
2025
Article DOI

The monodromy group of pq-covers

Carocca, Á.; Rodríguez, R.E.

Transform. Groups 30 (2025), no. 1, 147–164.

2024
Article DOI

On group actions on Riemann-Roch spaces of curves

Carocca, A.; Vásquez Latorre, D.

J. Pure Appl. Algebra 228 (2024), no. 2, Paper No. 107451, 12 pp.

2023
Article DOI

Abelian varieties and Riemann surfaces with generalized quaternion group action

Carocca, A.; Reyes-Carocca, S.; Rodríguez, R.E.

J. Pure Appl. Algebra 227 (2023), no. 11, Paper No. 107398, 26 pp.

2021
Article DOI

Decomposable Jacobians

Carocca, A.; Lange, H.; Rodríguez, R.E.

Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 4, 1673–1690.

Article DOI

Riemann surfaces of genus 1 + q² with 3q² automorphisms

Carocca, A.; Reyes-Carocca, S.

J. Algebra 588 (2021), 440–470.

Article DOI

q-étale covers of cyclic p-gonal covers

Carocca, Á.; Hidalgo, R.A.; Rodríguez, R.E.

J. Algebra 573 (2021), 393–409.

Article DOI

Equations for abelian subvarieties

Carocca, A.; Lange, H.; Rodríguez, R.E.

J. Algebra 565 (2021), 82–97.

2019
Article DOI

Étale double covers of cyclic p-gonal covers

Carocca, A.; Lange, H.; Rodríguez, R.E.

J. Algebra 538 (2019), 110–126.

Article DOI

Abelian varieties with finite abelian group action

Carocca, A.; Lange, H.; Rodríguez, R.E.

Arch. Math. (Basel) 112 (2019), no. 6, 615–622.

2018
Article DOI

On Galois group of factorized covers of curves

Carocca, A.; Romero Rojas, M.

Rev. Mat. Iberoam. 34 (2018), no. 4, 1853–1866.

Article DOI

Hecke algebras acting on abelian varieties

Carocca, A.; Rodríguez, R.E.

J. Pure Appl. Algebra 222 (2018), no. 9, 2626–2647.

2014
Article DOI

Symmetric group actions on Jacobian varieties

Carocca, A.; Rodríguez, R.E.; Rojas, A.M.

Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces, Contemp. Math., 629, Amer. Math. Soc., 43–57.

2013
Article DOI

Orbifolds with signature (0; k, kn−1, kn, kn)

Carocca, A.; Hidalgo, R.A.; Rodríguez, R.E.

Pacific J. Math. 263 (2013), no. 1, 53–85.

2011
Article

Jacobians with complex multiplication

Carocca, A.; Lange, H.; Rodríguez, R.E.

Trans. Amer. Math. Soc. 363 (2011), no. 12, 6159–6175.

2010
Article

Prym and Prym-Tyurin varieties: a group-theoretical construction

Carocca, A.; Lange, H.; Rodríguez, R.E.; Rojas, A.M.

In the tradition of Ahlfors-Bers. V, Contemp. Math., 510, Amer. Math. Soc., 49–60.

2009
Article

Prym-Tyurin varieties via Hecke algebras

Carocca, A.; Lange, H.; Rodríguez, R.E.; Rojas, A.M.

J. Reine Angew. Math. 634 (2009), 209–234.

Article

Prym-Tyurin varieties using self-products of groups

Carocca, A.; Lange, H.; Rodríguez, R.E.; Rojas, A.M.

J. Algebra 322 (2009), no. 4, 1251–1272.

Article

The quasi-superfluous elements of a group

Carocca, A.; Maier, R.

JP J. Algebra Number Theory Appl. 13 (2009), no. 1, 99–107.

Article

Products of Jacobians as Prym-Tyurin varieties

Carocca, A.; Lange, H.; Rodríguez, R.E.; Rojas, A.M.

Geom. Dedicata 139 (2009), 219–231.

2008
Article

Generalized Humbert curves

Carocca, A.; González-Aguilera, V.; Hidalgo, R.A.; Rodríguez, R.E.

Israel J. Math. 164 (2008), 165–192.

2006
Article DOI

Jacobians with group actions and rational idempotents

Carocca, A.; Rodríguez, R.E.

J. Algebra 306 (2006), no. 2, 322–343.

Article

Weyl groups and abelian varieties

Carocca, A.; González-Aguilera, V.; Rodríguez, R.E.

J. Group Theory 9 (2006), no. 2, 265–282.

2005
Article

Criteria for the solubility and non-simplicity of finite groups

Amberg, B.; Carocca, A.; Kazarin, L.

J. Algebra 285 (2005), no. 1, 58–72.

2002
Article

Dihedral groups acting on Jacobians

Carocca, A.; Recillas, S.; Rodríguez, R.E.

Complex manifolds and hyperbolic geometry, Contemp. Math., 311, Amer. Math. Soc., 41–77.

Article

A note on solvability of factorizable finite groups

Carocca, A.

Hokkaido Math. J. 31 (2002), no. 2, 343–348.

2000
Article

Solvability of factorized finite groups

Carocca, A.

Glasg. Math. J. 42 (2000), no. 2, 271–274.

1999
Article

Theorems of Kegel-Wielandt type

Carocca, A.; Maier, R.

Groups St. Andrews 1997 in Bath, I, London Math. Soc. Lecture Note Ser., 260, Cambridge Univ. Press, 195–201.

1998
Article

On a possible nonsimplicity criterion for finite factorized groups

Carocca, A.

Mat. Contemp. 14 (1998), 13–19.

Article

Hypercentral embedding and pronormality

Carocca, A.; Maier, R.

Arch. Math. (Basel) 71 (1998), no. 6, 433–436.

Article

On factorized finite groups in which certain subgroups of the factors permute

Carocca, A.

Arch. Math. (Basel) 71 (1998), no. 4, 257–261.

1997
Article

Some solvability criteria for finite groups

Carocca, A.; Matos, H.

Hokkaido Math. J. 26 (1997), no. 1, 157–161.

1996
Article

A note on the product of ℱ-subgroups in a finite group

Carocca, A.

Proc. Edinburgh Math. Soc. (2) 39 (1996), no. 1, 37–42.

1995
Article

A note on a theorem of W. Gaschütz and N. Itô

Carocca, A.

Bol. Soc. Brasil. Mat. (N.S.) 26 (1995), no. 2, 161–165.

1994
Article

Completeness properties of certain formations

Carocca, A.

Mat. Contemp. 6 (1994), 1–6.

1993
Article

The p-Huppert-subgroup and the set of p-quasi-superfluous elements in a finite group

Carocca, A.; Maier, R.

Proc. Edinburgh Math. Soc. (2) 36 (1993), no. 2, 289–297.

1992
Article

p-supersolvability of factorized finite groups

Carocca, A.

Hokkaido Math. J. 21 (1992), no. 3, 395–403.

04
Funding

Research Grants

FONDECYT Regular · 1240181

On Group actions on Surfaces and Varieties, and their linear representations on related geometric objects

Principal Investigator: Ángel Carocca
Funding: National Fund for Scientific and Technological Development (FONDECYT) Regular · ANID
Period: April 2024 – March 2028

Active

FONDECYT Regular · 1200608

On group representations and their actions on surfaces and varieties

Principal Investigator: Ángel Carocca
Funding: National Fund for Scientific and Technological Development (FONDECYT) Regular · ANID
Period: April 2020 – March 2024

Completed

MATH-AmSud · Código: MATH 2020014

Algebraic and geometric aspects of varieties and manifolds

Principal Investigator: Ángel Carocca
Funding: MATH-AmSud Program · ANID
Period: 2020

Completed

REDES · Código: 190140

South-North Latin American network through Geometry

Principal Investigator: Ángel Carocca
Funding: REDES Program · ANID
Period: 2019

Completed

ECOS-Sud · Código: ECOS 190030

Geometry of K3 surfaces

Principal Investigator: Ángel Carocca
Funding: ECOS-Sud Program · ANID
Period: 2019

Completed

MEC · Código: PAI80150021

Geometría de Grupos y Algebras (Invitado: Prof. Irina Markina, University of Bergen, Noruega)

Principal Investigator: Ángel Carocca
Funding: Advanced Human Capital Attraction from Abroad (MEC) · CONICYT
Period: 2015

Completed

FAPERJ–UFRO · Código: FPJ15-0001

La geometría de variedades complejas

Principal Investigator: Ángel Carocca
Funding: Bilateral Agreement FAPERJ–UFRO
Period: 2015 – 2017

Completed

FONDECYT Regular · 1130445

Group actions on complex Tori

Principal Investigator: Ángel Carocca
Funding: National Fund for Scientific and Technological Development (FONDECYT) Regular · CONICYT
Period: March 2013 – March 2017

Completed
05
Science and community

Outreach and Extension

Community Outreach Project

Murales y voces que inspiran: Mujer y Ciencia

Role: Collaborator  ·  Period: November 2024

Completed
06
Researcher Training

Graduate Supervision

Current Students

2019 –

Vicente Chicaiza (Advisor)

Ph.D. in Mathematical Sciences · Universidad de La Frontera, Temuco, Chile

Thesis: Automorfismos y endomorfismos de variedades abelianas

2025 –

Víctor Valdebenito (Co-advisor)

Doctorado en Ciencias mención Matemática · Universidad de La Frontera, Temuco, Chile

Graduated Students

2017

Jaime Pinto (Advisor)

Ph.D. in Mathematical Sciences · Universidad de Chile, Santiago, Chile

Thesis: Curvas de tipo Fermat

2013

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

2013

Daniela Vásquez (Advisor)

Ph.D. in Mathematical Sciences · Universidad de Chile, Santiago, Chile

Thesis: Acciones de grupos sobre el espacio de Riemann–Roch