Topological methods in algebraic geometry(Chinese Edition)

Paperback. Pub Date: November 2004 Pages: 234 in Publisher: World Publishing Company H. CARTAN and the J.-P. SERRE have shown how fundamental theoremson holomorphically complete manifolds (STEIN manifolds) can be for-mulated in terms of sheaf theory . These theorems imply many facts offunction theory because the domains of holomorphy are holomorphicallycomplete. They can also be applied to algeaic geometry because thecomplement of a hyperplane section of an algeaic manifold is holo-morphically complete. J.-P. SERRE has obtained important results onalgeaic manifolds by these and other methods. Recently many of hisresults have been proved for algeaic varieties defined over a field ofarbitrary characteristic. K. KODAIRA and DC SPENCER have alsoapplied sheaf theory to algeaic geometry with great success. Theirmethods differ from those of SERRE in that they use techniques fromdif...