Varieties which have two projective space bundle structures

Abstract

In this article w e study the structure of varieties w hich h a v e two bundle structures whose fibers are projective spaces. Well-known examples are PrX 1 3 s, P ( T ) a n d fiber product Ri X yR2 o f R , and R 2 o v e r Y w here R , and R , are ruled varieties over Y . T h e aim of this work is to classify such varieties under some additional conditions.