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 (Xt) of algebraic varieties, is the set of t for which Xt is rational open, closed?
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