Very Ampleness of Line Bundles and Canonical Embedding of Coverings of Manifolds |
| |
Authors: | Sai-Kee Yeung |
| |
Institution: | (1) Department of Mathematics, Purdue University, West Lafayette, IN, 47907, U.S.A. |
| |
Abstract: | Let L be an ample line bundle on a Kähler manifolds of nonpositive sectional curvature with K as the canonical line bundle. We give an estimate of m such that K+mL is very ample in terms of the injectivity radius. This implies that m can be chosen arbitrarily small once we go deep enough into a tower of covering of the manifold. The same argument gives an effective Kodaira Embedding Theorem for compact Kähler manifolds in terms of sectional curvature and the injectivity radius. In case of locally Hermitian symmetric space of noncompact type or if the sectional curvature is strictly negative, we prove that K itself is very ample on a large covering of the manifold. |
| |
Keywords: | very ampleness canonical embedding |
本文献已被 SpringerLink 等数据库收录! |
|