HOLOMORPHIC EMBEDDINGS OF STEIN SPACES IN INFINITE-DIMENSIONAL PROJECTIVE SPACES

Title & Authors
HOLOMORPHIC EMBEDDINGS OF STEIN SPACES IN INFINITE-DIMENSIONAL PROJECTIVE SPACES
BALLICO E.;

Abstract
Lpt X be a reduced Stein space and L a holomorphic line bundle on X. L is spanned by its global sections and the associated holomorphic map $\small{h_L\;:\;X{\to}P(H^0(X, L)^{\ast})}$ is an embedding. Choose any locally convex vector topology $\small{{\tau}\;on\;H^0(X, L)^{\ast}}$ stronger than the weak-topology. Here we prove that $\small{h_L(X)}$ is sequentially closed in $\small{P(H^0(X, L)^{\ast})}$ and arithmetically Cohen -Macaulay. i.e. for all integers $\small{k{\ge}1}$ the restriction map $\small{{\rho}_k\;:\;H^0(P(H^0(X, L)^{\ast}),\;O_{P(H^0(X, L)^{\ast})}(k)){\to}H^0(h_L(X),O_{hL_(X)}(k)){\cong}H^0(X, L^{\otimes{k}})}$ is surjective.
Keywords
Stein space;infinite-dimensional complex projective space;infinite Grassmannian;arithmetically Cohen-Macaulay;
Language
English
Cited by
References
1.
H. Grauert and R. Remmert, Theory of Stein Spaces, Springer, Berlin-Heidelberg- New York, 1979

2.
R. C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1965

3.
H. H. Schaefer, Topological Vector Spaces, Springer, Berlin-Heidelberg-New York, 1999