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Audiovisual Mathematics Library

Audiovisual Mathematics Library

Documents 14E07 3 results

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Periods of polarized hyperkähler manifolds​ - Debarre, Olivier (Author of the conference) | CIRM H

Post-edited

Hyperkähler manifolds are higher-dimensional analogs of K3 surfaces. Verbitsky and Markmann recently proved that their period map is an open embedding. In a joint work with E. Macri, we explicitly determine the image of this map in some cases. I will explain this result together with a nice application (found by Bayer and Mongardi) to the (almost complete) determination of the image of the period map for cubic fourfolds, hereby partially recovering a result of Laza.[-]
Hyperkähler manifolds are higher-dimensional analogs of K3 surfaces. Verbitsky and Markmann recently proved that their period map is an open embedding. In a joint work with E. Macri, we explicitly determine the image of this map in some cases. I will explain this result together with a nice application (found by Bayer and Mongardi) to the (almost complete) determination of the image of the period map for cubic fourfolds, hereby partially ...[+]

14C34 ; 14E07 ; 14J50 ; 14J60

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Signature morphisms from the Cremona group - Zimmermann, Susanna (Author of the conference) | CIRM H

Multi angle

The plane Cremona group is the group of birational transformations of the projective plane. I would like to discuss why over algebraically closed fields there are no homomorphisms from the plane Cremona group to a finite group, but for certain non-closed fields there are (in fact there are many). This is joint work with Stéphane Lamy.

14E07 ; 14E30

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Action of the Cremona group on a CAT(0) cube complex - Lonjou, Anne (Author of the conference) | CIRM H

Virtualconference

The Cremona group is the group of birational transformations of the projective plane. Even if this group comes from algebraic geometry, tools from geometric group theory have been powerful to study it. In this talk, based on a joint work with Christian Urech, we will build a natural action of the Cremona group on a CAT(0) cube complex. We will then explain how we can obtain new and old group theoretical and dynamical results on the Cremona group.

14E07 ; 20F65 ; 20F67

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