Existence of a line without real points in quadric intersection

Abstract

The topology of the intersection of three quadrics in Euclidean 6-space is studied using Kollar results. This needs an existence of a line without real points in the complex projectivisation of quadrics. We establish the existence of such a line under some assumptions. It is a step to obtain a list of all possible homeomorfism types of manifolds under consideration.

5 pages, in russian