Emre Sertöz (MPI Leipzig)
Tuesday, May 8, 2018 - 13:15
HU, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin-Adlershof, 3.006, Erdgeschoss
Forschungsseminar "Arithmetische Geometrie"
Prof. Dr. Jürg Kramer, Prof. Dr. Thomas Krämer
The periods of a complex projective manifold X are complex numbers, typically expressed as integrals, which give an explicit representation of the Hodge structure on the cohomology of X. Although they provide great insight, periods are often very hard to compute. In the past 20 years, an algorithm for computing the periods existed only for plane curves. We will give a different algorithm which can compute the periods of any smooth projective hypersurface and can do so with much higher precision. As an application, we will demonstrate how to reliably guess the Picard rank of quartic K3 surfaces and the Hodge rank of cubic fourfolds from their periods.
submitted by Kristina Schulze (schulze@math.hu-berlinde)