## 超越数論セミナー

タイトル The Hilbert Property and the topology of algebraic varieties 2018年3月9日 13:30―15:30 Pietro Corvaja 氏 (University of Udine) 矢上キャンパス 14棟７階　14 - 733 he celebrated Hilbert Irreducibility Theorem can be formulated by saying that a morphism from a curve to the line cannot be surjective on the set of rational points, unless it admits rational sections. We say that an algebraic variety $X$ satisfies the Hilbert Property over a number field $k$ if for every generically finite morphism $\pi: Y\to X$ without rational section, the image of $k$-rational points of $Y$ does not cover the whole set $X(k)$. After Hilbert Irreducibility Theorem, the line, and also every other rational algebraic variety, has the Hilbert Property over $Q$. In a joint recent work with U. Zannier, we investigated which algebraic varieties can share this property, connecting it with the topology of their set of complex points.