Let X be a projective algebraic variety, the set of solutions of a system of homogeneous polynomial equations. Several classical notions describe how “unconstrained” the solutions are, i.e., how close X is to projective space: there are notions of rational, unirational and stably rational varieties. Over the field of complex numbers, these notions coincide in dimensions 1 and 2, but diverge in higher dimensions. In this talk I will discuss classical and recent advances in this area, examples and deformation properties.
This video is part of Harvard University‘s conference JDG 2017.
