Speaker: Emilia Mezzetti
Title: Focal loci of families of algebraic varieties
Abstract: Motivated by examples in classical differential geometry and in ODE, we introduce the notion of focal locus (or focal scheme) for an algebraic family F of subvarieties of the projective space. We are interested in particular in studying families of linear spaces. Let X be the union of the spaces of F. If X is a proper subvariety, then we show how the existence and the shape of the focal locus is related to the tangential behaviour of X. We give also some example of families of linear spaces filling up the whole projective space and their interpretation in terms of varieties of multisecant lines.