This is the first version of a workshop, organized by the Doctoral Program in Mathematics of Universidad de Concepción, which brings together researchers in Geometry from various Chilean Universities and with the participation of researchers from foreign Institutions. On this occasion, the speakers will be (* = to be confirmed):

Programa

JUEVES 23 NOVIEMBRE – Sala FM-202

  • 10.15 – 11.00: Martina Monti
  • Cafe’
  • 11.30 – 12.15:  Antonio  Laface

VIERNES 24 NOVIEMBRE – Auditorio CFM

  • 10.15 – 11.00: Saúl Quispe
  • Cafe’
  • 11.30 – 12.15: Daniel Pellicer

Titles and abstracts

Cox rings of blowing-ups. Antonio Laface

Abstract: Let R := C[x_1,…,x_r] and let G be a group that acts linearly on R. Hilbert’s fourteenth problem asks when the invariant subalgebra R^G is finitely generated. This is true for reductive groups. However, in 1959, Nagata presented a counterexample where G is a subgroup of the additive group C^r and R has 2r variables. He proves that R^G is isomorphic to the Cox ring of the blowup of a projective space of dimension r-dim(G)-1 at r points defined by the equations that cut G in C^r. Thus, he provides examples of non-finite generation. Following this example, research began on the finite generation of Cox rings from blowups of toric varieties (generalizations of projective space) at points. In this talk, I will discuss recent results on toric surfaces.

Teselaciones euclidianas muy simétricas con piezas cuya frontera es fractal. Daniel Pellicer

Abstract: Presentaremos un método para construir algunas teselaciones euclidianas donde cualquier par de piezas son trasladadas una de la otra, y además cumplen con que la frontera de cada una de ellas es fractal.

Quasi-abelian group acting on pseudo-real Riemann surfaces. Saúl Quispe

Abstract: disponible aquí

Automorphisms and quotients of Calabi-Yau threefolds of type A. Martina Monti.

Abstract: Calabi-Yau manifolds of type A provide an interesting setting in which it’s possible to study relations between Calabi-Yau manifolds and Abelian varieties, indeed these manifolds are defined as the quotient of an abelian variety A by a free action of a finite group G.In dimension 3 there is a full classification of these manifolds: the only possibilities for the group G are (Z/2Z)^2 and D_4 the dihedral of order 8.
The aim of this talk is to present the results concerns the full classification of automorphism group and quotients of the Calabi-Yau 3folds of type A.First, we introduce the two possible (irreducible) families of these manifolds that appear in dimension 3 and briefly recall the construction. Then, we move to the classification of automorphisms group of such Calabi-Yau 3folds providing also a result that characterizes the automorphism group of Calabi-Yau manifolds of type A. Finally, we only state the result about the quotients of the Calabi-Yau 3folds A/D_4 pointing out some consequences.