Über allgemeine Hyperflächenschnitte einer algebraischen Varietät

Abstract

LetV/k be an irreducible algebraic variety over a fieldk in an affinen-space andF u a generic hypersurface defined byu 1 f 1 (X)+...+u r f r(X)=0, whereu 1...,u r are indeterminates overk andf 1(X), ...,f r(X) are polynomials ink[X 1, ...,X n]. Let (E) be a property which an arbitrary algebraic variety could have, e. g. irreducibility, normality (local or global), ... Then it will be studied under which conditions off 1(X), ...,f r(X) (E) may be transfered fromV/k toV∩F u /k(u) (and conversely).