Open AccessVanishing Theorems on Complete Kähler Manifolds
Author(s) -
Takeo Ohsawa
Publication year - 1984
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195181825
Subject(s) - mathematics , sheaf , square integrable function , section (typography) , pure mathematics , kähler manifold , cohomology , complex manifold , vector bundle , holomorphic function , dimension (graph theory) , hermitian matrix , comparison theorem , manifold (fluid mechanics) , complex dimension , advertising , mechanical engineering , engineering , business
Let X be a complex manifold of dimension n and let E be a holomorphic vector bundle over X. We shall here try to continue the study on the vanishment of the sheaf cohomology groups H(X3 0(E)) which has been performed by Kodaira [10], [11], GrauertRiemenschneider [5], Andreotti-Vesentini [1], [2], Nakano [14], [15], Kazama [9], and others. The purpose of the present paper is to study the cohomology groups on complete Kahler manifolds. Although the spirit is the same as in [1] and [14], we restrict ourselves to L-cohomology groups' and aim at finding a proper subspace of L-forms for which 8-equation is solvable. We shall prove the following theorem.
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