Research Center - Geometry at the Frontier

 
Workshop Geometry at the Frontier III 1/2 was held with great success in Pucón
between November 29 and December 2, 2022.

Research Center

Geometry at the Frontier 

A pole of development in southern Chile

RECENT NEWS  

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Wednesday, 21 july 2021
2nd ECOS-ANID Workshop on Algebraic Geometry was successfully developed. 

The event summoned more than 40 attendees and consisted of eight speakers from France, United States, Italy, Democratic Republic of the Congo, [View more...]
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Thursday, 10 June 2021
Researchers and PhD students meet in the first Workshop on Hyperbolic Geometry (USA-Chile). 

For the purpose of sharing research advances and encouraging future work among the academic community, students and researchers from all over [View more...]
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Monday, 31 May 2021
Great success on the South-North Latin American Workshop on Geometry I.  

During the 26th, 27th and 28th of May 2021, successfully brought the first workshop "South-North Latin American Workshop on Geometry", organized [View more...]

We deepen knowledge of Complex Geometry and its Applications 

Team

The local researchers that form our center
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Research

A closer look at our scientific production
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Recent publications  

Stable Riemann orbifolds of Schottky type

DOI: 10.1007/s13398-021-01052-0 | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | Published: 6 May 2021

Raquel Díaz and Rubén A. Hidalgo

ABSTRACT
In this paper we study the Galois group of the Galois cover of the composition of a q-cyclic étale cover and a cyclic p-gonal cover for any odd prime p. Furthermore, we give properties of isogenous decompositions of certain Prym and Jacobian varieties associated to intermediate subcovers given by subgroups.

q-étale covers of cyclic p-gonal covers

DOI: 10.1016/j.jalgebra.2020.12.033 | Journal of Algebra | Published: 1 May 2021

Angel Carocca, Rubén A. Hidalgo and Rubí E. Rodríguez

ABSTRACT
In this paper we study the Galois group of the Galois cover of the composition of a q-cyclic étale cover and a cyclic p-gonal cover for any odd prime p. Furthermore, we give properties of isogenous decompositions of certain Prym and Jacobian varieties associated to intermediate subcovers given by subgroups.

Mirror symmetry for K3 surfaces

DOI: 10.1007/s10711-020-00548-0 | Geometriae Dedicata | Published: 04 July 2020

C. J. Bott, Paola Comparin and Nathan Priddis

ABSTRACT
For certain K3 surfaces, there are two constructions of mirror symmetry that appear very different. The first, known as BHK mirror symmetry, comes from the Landau–Ginzburg model for the K3 surface; the other, known as LPK3 mirror symmetry, is based on a lattice polarization of the K3 surface in the sense of Dolgachev’s definition. There is a large class of K3 surfaces for which both versions of mirror symmetry apply. In this class we consider the K3 surfaces admitting a certain purely non-symplectic automorphism of order 4, 8, or 12, and we complete the proof that these two formulations of mirror symmetry agree for this class of K3 surfaces.

Geometric description of virtual Schottky groups

DOI: 10.1112/blms.12346 | Bulletin of the London Mathematical Society | Published: 15 May 2020

Rubén A. Hidalgo

ABSTRACT
A virtual Schottky group is a Kleinian group K containing a Schottky group G as a finite index normal subgroup. These groups correspond to those groups of automorphisms of closed Riemann surfaces which can be realized at the level of their lowest uniformizations. In this paper, we provide a geometrical structural decomposition of K. When K/G is an abelian group, an explicit free product decomposition in terms of Klein–Maskit's combination theorems is provided.
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