N-dimensional Smooth Fano Variety With Pseudo-index Not Less Than N-2

Let X be a smooth Fano variety of dimension n over the complex number field and L be an ampleline bundle on X.l（X） denotes pseudo-index of Fano variety X,which is defind byl（X）=min{-K_X,C|C isa rational curve of X}. We study X for l （X）=n-1,and we show thatX is one of the following:（ⅰ） X is a Pⁿ² bundle over a smooth surface.（ⅱ） X is a Pⁿ¹ bundle over a smooth curve.（ⅲ） X is a Qⁿ¹ bundle over a smooth curve.（ⅳ） For a general fiber F of X,（F, L_F）is a Del Pezzo manifold.WhereLF is the restrictionof the ample line bundle L on the general fiber F.Let X be a smooth Fano variety of dimension n over the complex number field and L be an ampleline bundle on X. We study X for l （X）=n-2,and we show that X is a Pⁿ¹ bundle over asmooth curve etc.