Euisung Park, On Rank 3 Quadratic Equations of Projective Varieties

Many projective varieties are ideal-theoretically cut out by quadratic polynomials of rank less than or equal to 4. Classical constructions in projective geometry like rational normal scrolls and Segre-Veronese varieties are examples. Regarding this phenomenon, I would like to talk about the following two results in this talk. First, there are many projective varieties cut out ideal-theoretically by quadratic polynomials of rank 3. Second, there is a nice structure of the locus of rank 3 quadratic equations of a projective variety.