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郭婷婷 ( National Taiwan University )
2022-08-18  14:00 - 16:00
Room 201, Astronomy and Mathematics Building

In this section, we define a relative version of nonsingular variety over a field k, that is, the smooth morphism. We first give some basic results about smooth morphisms. Next, we investigate the equivalent conditions for a morphism of nonsingular varieties being smooth. Moreover, if the field k is algebraically closed and of characteristic zero, we get the generic smoothness theorem. We define group variety and homogeneous space, and prove the theorem of Kleiman. Finally, we get the characteristic 0 Bertini theorem as a consequence.