Pseudoindex为n-1的光滑n维Fano簇

摘要

X is complex field of smooth N-dimensional FANO clusters, X is defined as the overall length l(X) = min{-Kx · CC is a rational curve on X}, if l{X)=n - 1 , X is the one of five results:(l) X is a smooth bundle on Pn-2(2)X is a smooth bundle on Pn-1 (3)X is a smooth bundle on Qn-1 (4)X is Del Pezzo manifold(5) F is the general fiber of X , (F,LF) is Del Pezzo manifold%X是复数域上的光滑n维Fano簇,X的整体长度定义为l(X)=min{-Kx·C│C是X上的有理曲线},如果l(X)=n-1,则X是以下五者之一:(1)X是光滑曲面上的pn-2丛;(2)X是光滑曲线上的Pn-1丛;(3)X是光滑曲线上的Qn-1丛;(4)X是Del Pezzo流形;(5)对于X的一般纤维F,(F,LF)是Del Pezzo流形.其中,LF是X上的丰富线丛L在一般纤维F上的限制.