Date: 9월 14일 화요일 오후 04:00-05:00 Place: Online (zoom) https://us02web.zoom.us/j/81228525316?pwd=NjRZKzhZK3ZueUs4SEZyR2FkbDlkdz09 ID : 812 2852 5316 PASSWD : 357406 Speaker : Victor Gonzalez Alonso (University of Hannover) Title: Flat and kernel subbundles of PVHS for families of curves. Abstract: Given a family of smooth complex projective curves, its associated polarized variation of Hodge structure contains a natural maximal flat unitary subbundle U. This bundle plays an important role in the study of fibred surfaces and totally geodesic subvarieties of the Jacobian locus. The main obstacle to study U is that it is defined by conditions on open subsets of the base, but there is no useful characterization of its fibre at any (general) point. A possible first approximation is to consider the kernel K of the associated Higgs field, which contains the flat subbundle U and whose fibres can be determined pointwise. In this talk I will present some joint results with Sara Torelli, showing on the one hand that K can be arbitrarily bigger than U, and on the other hand defining additional morphisms of vector fields (some kind of generalized Higgs fields) whose kernels define U. Time permitting, I will comment how the first additional such vector field can be related to some sort of second order Kodaira-Spencer classes of the family.