Dual Varieties: Old Stuff, New Perspectives

Location: Department of Mathematics, via Sommarive, 14 - Povo (TN) - Aula Seminari
From 10:00 a.m.

Speaker:

• Roberto Muñoz (Universidad Rey Juan Carlos)

Abstract: 
It is quite natural in projective geometry to associate to a variety X in P^N its dual variety X* in P^N*, which parametrizes tangent hyperplanes to X. Several problems on dual varieties are of interest, in particular, the classification of those smooth varieties whose dual is not a hypersurface (dual defective varieties). We will revisit some results on this classification, mainly those based on the study of the linear spaces (the so called contact locus) contained in X. This is naturally related with modern problems on uniruled varieties and the relation goes in both directions: results on duals are applied to characterize some Fano varieties and results on families of rational curves are used to classify some dual defective varieties.

Reference person: Eduardo Luis Sola Conde