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• W2064466899 abstract "The Moisezon theorem is extended to complex spaces with isolated singularities. A problem of fundamental concern is determining sufficient conditions under which a complex space X is algebraic. Ideally, these conditions involve simple intrinsic analytic features of X . An n-dimensional manifold X is called Kahler if it admits a hermitian metric whose associated (1, 1)-form co is closed, and it is called Mois'ezon if it admits n algebraically independent global meromorphic functions. A fundamental theorem of Moisezon states that if a manifold X is Kahler and Moisezon, then X is a projective algebraic variety (i.e., X is the common zero locus of a set of homogeneous polynomials in projective space). The Kahler and Moisezon conditions can be generalized to singular complex spaces; however, it is no longer the case that these two conditions will imply algebraicity (an example is provided in [7]). In this paper we investigate situations under which a complex space X which is Kahler and Moisezon must be projective algebraic. For example, we show that if a compact space of dimension at least four is a complete intersection with isolated singularities, then the Kahler and Moisezon conditions imply projective algebraicity. In Section 1 we investigate conditions which allow us to extend holomorphic line bundles over singular points of a complex space. In Section 2 we use a singular version of the Kodaira embedding theorem to reduce the problem to one of extending line bundles over singular points. 1. EXTENDING LINE BUNDLES OVER SINGULAR POINTS Let X be a complex space with isolated singularities and structure sheaf Ax . Recall that an invertible sheaf is a locally free Ax-module of rank one and that the set of these is the Picard group H1 (X, Ax) . We seek sufficient conditions for a holomorphic line bundle L on the regular part of X to extend to X as an invertible sheaf. For a small neighborhood U of a singularity x E X, the exact sequence of sheaves 0 -Z -Ax -A -x 0 and the exact sequence Received by the editors June 7, 1993. 1991 Mathematics Subject Classification. Primary 32J25." @default.
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• W2064466899 date "1995-03-01" @default.
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• W2064466899 title "Kähler Moišezon spaces which are projective algebraic" @default.
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• W2064466899 doi "https://doi.org/10.1090/s0002-9939-1995-1242109-7" @default.
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