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Variedades de Calabi–Yau

Numerical transcendental methods for computing Picard and Hodge groups
Emre Sertoz

Max Planck Institute for Mathematics in the Sciences
Terça-feira, 9 de outubro de 2018, 15:30
Sala 224
Based on high precision computation of periods and lattice reduction techniques, we compute the Picard group of smooth surfaces in P3. The approach applies more generally to the computation of the lattice generated by Hodge cycles of middle dimension on smooth projective hypersurfaces. Although the results cannot be proven correct, they rely on outstanding numerical evidence. The exceptional conditions that would lead to miscomputation are quantified. As a by product, we can count the number of quadric curves and twisted cubics lying on a given smooth quartic surface (K3) and compute the endomorphism rings of its transcendental lattice. This is joint work with Pierre Lairez.