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Kawamata-Viehweg vanishing theorem for compact Kähler manifolds. (English) Zbl 0797.53052
Mabuchi, Toshiki (ed.) et al., Einstein metrics and Yang-Mills connections. Proceedings of the 27th Taniguchi international symposium, held at Sanda, Japan, December 6-11, 1990. New York: Marcel Dekker, Inc.. Lect. Notes Pure Appl. Math. 145, 59-68 (1993).
The Kodaira vanishing theorem is generalized by Y. Kawamata [Math. Ann. 261, 43-46 (1982; Zbl 0476.14007)] and E. Viehweg [J. Reine Angew. Math. 335, 1-8 (1982; Zbl 0485.32019)] to nef line bundles over projective manifolds and J. Kollár [Ann. Math., II. Ser. 123, 11- 42 (1986; Zbl 0598.14015)] showed that the multiplication by a holomorphic section of a line bundle over a projective algebraic manifold induces injective homomorphisms between cohomology groups of the line bundle provided that certain tensor power of this line bundle is generated by global sections. The present paper extends both vanishing and injectivity theorems to compact Kähler manifolds.
For the entire collection see [Zbl 0772.00032].
Reviewer: C.-L.Tiba (Iaşi)

53C55 Global differential geometry of Hermitian and Kählerian manifolds