**Forschungsseminar "Algebraische Geometrie"**

Prof. Dr. Gavril Farkas, Prof. Dr. Bruno Klingler

#### 13:15 - 14:15 Andrey Soldatenkov (Uni Bonn), 14:45 - 15:45 Francesco Russo (Uni Catania)

## Russo: Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds, Soldatenkov: Kuga-Satake construction under degeneration

**Programm / Abstract:**

Soldatenkov: Degree two cohomology H of any projective K3 surface carries a polarized Hodge structure with one-dimensional (2,0)-component. The Kuga-Satake construction attaches to it an abelian variety A and an embedding of H into the second cohomology of A, compatible with Hodge structures. I will talk about our joint work with S.Schreieder, where we study the behaviour of Kuga-Satake abelian varieties for degenerating families of K3 surfaces.
Russo: Kuznetsov Conjecture and the work of Hassett predict that a general cubic fourfold belonging to an irreducible divisor C_d parametrizing smooth cubic fourfolds of discriminant d is rational if and only if d is an admissible value in the sense of Hassett, that is, if and only if d>6 is an even integer not divisible by 4, by 9 nor by any odd prime of the form 2+3m. I will present a proof of this conjecture for the smallest admissible values d=26 and d=38 (the case d=14 being classical), via the construction of a congruence of 5-secant conics to a surface contained in the general element of C_d for the respective values of d. This is joint work with Giovanni Staglianò.

**Zeit:**

am Mittwoch den 14. Februar 2018 um 13:00

**Ort:**

HU, Institut für Mathematik

Rudower Chaussee 25

12489 Berlin-Adlershof

1.114 1. Stock

*eingetragen von Kristina Schulze(schulze@math.hu-berlin.de, )*

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