Research Center

Geometry at the Frontier 

A pole of development in southern Chile

RECENT NEWS  

Friday, 22 January 2021
Dr. Emilio Lauret at Universidad Nacional del Sur, Bahía Blanca (Argentina) gave the talk “Can one hear the shape of a drum?".

Friday, 08 January 2021
Researchers at the center Geometry at the Frontier obtains MATH AmSud grant in joint with Universities of Argentina, Brazil and France [View more...]
Thursday, 07 January 2021
Dr. Ángel Carocca, researcher at Center Geometry at the Frontier, gave the talk “Galois group of pq-covers" in the first session of the year of the Cruz del Sur Seminar.


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We deepen knowledge of Complex Geometry and its Applications 

Team

The local researchers that form our center

Research

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Recent publications  

Sub-Riemannian Geodesics on Nested Principal Bundles

DOI: 10.1007/978-3-030-58653-9_8 | CONTROLO 2020 | Published: 09 September 2020

Mauricio Godoy Molina and Irina Markina

ABSTRACT
We study the interplay between geodesics on two non-holonomic systems that are related by the action of a Lie group on them. After some geometric preliminaries, we use the Hamiltonian formalism to write the parametric form of geodesics. We present several geometric examples, including a non-holonomic structure on the Gromoll-Meyer exotic sphere and twistor space.

Equations for abelian subvarieties

DOI: 10.1016/j.jalgebra.2020.07.030 | Journal of Algebra | Published: 05 September 2020

Angel Carocca, Herbert Lange and Rubí E. Rodríguez

ABSTRACT
Given a finite group G and an abelian variety A acted on by G, to any subgroup H of G, we associate an abelian subvariety  on which the associated Hecke algebra  for H in G acts. Any irreducible rational representation of induces an abelian subvariety of  in a natural way. In this paper we give equations for this abelian subvariety. In a special case these equations become much easier. We work out some examples.

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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