中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

综合报告会

（Colloquium）

报告人：Prof. Olivier Debarre(法国巴黎高师)

题  目：Rationality of algebraic varieties

时  间：2018.05.18(星期五) , 15:30-16:30(15:00-15:30为茶点时间, 地点: 数学院南楼N920室)

地  点：数学院南楼N913室

注：该讲座茶点受到中链科技有限公司的资助

摘 要：

In algebraic geometry, one says that an algebraic variety X defined over a field K is rational if it is very close to being the affine space Kⁿ. This means that one can parametrize the points of X by Kⁿ, in an almost one-to-one fashion.

Deciding whether an algebraic variety, given by polynomial equations, is rational is in general very difficult.

I will start with very classical and elementary examples (like the rational parametrization of the circle) and move on to spectacular results obtained recently on the behavior of rationality in a family: given a family (X_t) of algebraic varieties, is the set of t for which X_t is rational open, closed?