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 one and two, but diverge in higher

dimensions. In this talk I will discuss classical examples of

rational and nonrational varieties, as well as recent advances in this

area.

### Algebra Seminar

Monday, April 10, 2017 - 3:15pm

#### Alena Pirutka

Courant Institute, NYU