Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Olivier Debarre
Inviter:
Title:
Rationality of algebraic varieties
Time & Venue:
2018.5.18 15:30-16:30 N920
Abstract:
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?
Appendix：
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