Existence of a line without real points in quadric intersection
  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. 
I. Shnurnikov
math.AG