|タイトル||The Hilbert Property and the topology of algebraic varieties|
|講演者||Pietro Corvaja 氏 (University of Udine)|
|場所||矢上キャンパス 14棟７階 14 - 733|
|内容||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.