Structure Of Birational Contractions On Projective Varieties

Let X be a nonsingular projective variety of dimension n, L be an ampleline bundle over X andK_X be the canonical bundle over X. Let f:X→Ybethe birational contraction from X to variety Y. AndK_X+mLbe thesupporting divisor of the former morphism f:X→Yfor some positiveinteger m≧1. F is a generic fiber of f. If dim F=m+1, then eachirreducible component of F is isomorphic to projective space P^m+1 orhyperquadric surface Q^m+1.