Study on equivariant mapps of toric varieties and vector bundles

对伴随丛无效的非奇异环面3-折叠上的充裕线丛进行了分类，并证明了这些充裕线丛是正常生成的。当伴随丛是有效的时，我们刻画了伴随丛的整体截面空间。由此，我们证明了伴随丛有效但不大的充裕线丛的正规生成，并证明了奇异环面上的充盈线丛和NEF线丛的整体截面的乘法映射是满射的。利用这一满足性，我们可以研究某一奇异环面3-折叠上的充盈线丛的正常生成，并成功地证明了环面弱Fano 3-折叠上的任何充盈线丛都是正常生成的。

We classify ample line bundles on nonsingular toric 3-folds whose adjoint bundles are not effective and prove that those ample line bundles are normally generated. We characterize the space of the global sections of the adjoint bundle when it is effective. From this we prove the normal generation of ample line bundle whose adjoint bundle is effective but not big.We also prove that the multiplication map of global sections of an ample line bundle and a nef line bundle on a singular toric surface is surjective. We may use this surjectivity to investigate normal generation of ample line bundles on a certain singular toric 3-fold.Moreover, we succeeded to prove that any ample line bundles on toric weak Fano 3-folds are normally generated.