A study on the dimension of global sections of adjoint bundles of polarized manifolds by the sectional geometric genus

设X是复数域上n维的光滑射影簇，L是X上的充分线丛，则称这对(X，L)为极化流形。本文研究了一个满足以下性质的整数m：对于伴随丛K_X+L为nef的四维极化流形(X，L)，m(K_X+L)有一个整体截口。证明了如果m大于或等于3，则m(K_X+L)有一个整体截口。此外，我们还证明了这种方法可以应用于n小于或等于11的情形。我们还研究了极化流形的一些不变量。这些结果对研究伴随丛的整体截面维是有用的。

Let X be a smooth projective variety of dimension n over the field of complex numbers and let L be an ample line bundle on X. Then we call this pair(X, L) a polarized manifold. In this investigation, we studied an integer m which satisfies the following property : for any 4-dimensional polarized manifolds(X, L) whose adjoint bundle K_X+ L is nef, m(K_X+ L) has a global section. We proved that if m is greater than or equal to 3, then m(K_X+ L) has a global section. Furthermore we proved that we can apply this method to the case where n is less than or equal to 11. We also studied some invariants of polarized manifolds. These results will be useful for the study of the dimension of global sections of adjoint bundles.