MIT Number Theory Seminar

SPEAKER:  Emre Sertöz  (MPI MiS Leipzig)

TITLE:  On reconstructing subvarieties from their periods

ABSTRACT: 

Recent advances allowed for high precision approximation of the periods of hypersurfaces. Using lattice reduction techniques such as LLL one can then heuristically compute the lattice of integer relations between the periods.  Each integral relation corresponds to a Hodge cycle on the hypersurface.  We give an algorithm which takes a (heuristic) integral relation (i.e. Hodge cycle) and attempts to reconstruct the ideal of a subvariety whose cohomology class represents the given Hodge cycle. We describe the conditions in which the algorithm is guaranteed to work and we demonstrate the practicality of the method by reconstructing conics and twisted cubics in quartic surfaces from their periods. This is joint work with Hossein Movasati.