# Journées de Géométrie Algébrique Poitiers-Bordeaux

24-25 November 2016
Poitiers
Europe/Paris timezone

## Hypersurfaces in projective schemes and Bertini's theorem

24 Nov 2016, 09:30
50m
0-6 (Poitiers)

Board: 1
Exposé de 50 min

Prof. Qing Liu

### Description

Let $X$ be a projective scheme over an affine base. We develop a technique for proving the existence of closed subschemes $H$ with various favorable properties. We offer several applications of this technique, including the existence of hypersurfaces in $X$ containing a given closed subscheme and intersecting properly a given closed set, and the existence of finite quasi-sections. This is joint work with O. Gabber and D. Lorenzini.

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