SEMINARIO 2021/11 CRUZ DEL SUR

Connected algebraic groups acting on Fano fibrations over P1

Viernes 09 de Julio. Vía ZOOM UFRO. 12:00 Hrs.

Conferencista: Enrica Floris. Université de Poitiers, Francia.

 Abstract

LetGbe a connected algebraic group andXa variety endowed with a regular action ofGand a Mori fibre spaceX/P1whose fibre is a Fano variety of Picard rank at least 2. Inthis talk I will explain why there is a proper horizontal subvariety ofXwhich is invariantunder the action ofG, alongside with some applications of this result to the classificationof connected algebraic subgroups of the Cremona group in dimension 4. This is a jointwork with J ́er ́emy Blanc.

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SEMINARIO 2021/10 CRUZ DEL SUR

Extremal Riemann surfaces and their properties

Viernes 25 de Junio. Vía ZOOM UFRO. 11:00 Hrs.

Conferencista: Ewa Kozłowska-Walania. University of Gdansk, Gdansk, Polonia.

 Abstract

A closed Riemann surface of genusg≥2 shall be calledextremalif it admits themaximal possible number of non-conjugate symmetries or if it admits the maximal numberof ovals for a set of non-conjugate symmetries with fixed points. These cases are to becalled s-extremal and o-extremal respectively. We shall present a variety of recent resultsconcerning such surfaces, in particular we show the structure of the automorphism groupin both s-and o-extremal case and find all the possible topological types of commutingsymmetries together with their defining equations in an o-extremal configuration. Specialattention shall be paid to the surfaces of even genera and in particular the so-calledbutton-likesurfaces, being unique both s-and o-extremal surfaces of genusg= 4k, k≥1 with anon-abelian automorphism group

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SEMINARIO 2021/09 CRUZ DEL SUR

Un algoritmo de descomposición para el cálculo de los impuestos sobre la renta con entidades de paso y su aplicación al caso chileno

Viernes 18 de Junio. Vía ZOOM UFRO. 16:00 Hrs.

Conferencista: Javiera Barrera. Universidad Adolfo Ibáñez, Santiago, Chile.

 Abstract

By applying the Ince Transformation, we establish exact travelling wavessolutions to the nonlinear evolution equation Benney-Lin type

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SEMINARIO 2021/08 CRUZ DEL SUR

Exact solution for a Benney-Lin equation type

Viernes 4 de Junio. Vía ZOOM UFRO. 16:00 Hrs.

Conferencista: Octavio Paulo Vera Villagran. Universidad de Tarapacá, Chile

 Abstract

By applying the Ince Transformation, we establish exact travelling wavessolutions to the nonlinear evolution equation Benney-Lin type

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SEMINARIO 2021/07 CRUZ DEL SUR

Manifolds with trivial canonical bundle:automorphisms and quotients

Viernes 14 de Mayo. Vía ZOOM UFRO. 11:00 Hrs.

Conferencista: Alice Garbagnati. Università degli Studi di Milano, Italia.

 Abstract

The manifolds with trivial canonical bundle are quite different with respect to theothers and they are essentially of three different types (tori, Calabi-Yau and hyperkahlermanifolds). Even if they are projective they do not admit a canonical projective model,hence in order to study their geometry one can not restrict to a specific projective model.Due to this (and other) peculiarity some specific techniques are used to analyze thesemanifolds. We first describe general results and constructions and we observe that thereare strong relations between different kinds of manifolds with trivial canonical bundle, inparticular related with the quotients by certain automorphisms. Then we consider thespecial case of hyperkahler 4-folds and of their automorphisms and we describe some oftheir quotients.

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