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Holomorphic cohomology groups on compact Kähler complex spaces

✍ Scribed by Vincenzo Ancona; Bernard Gaveau

Publisher
Elsevier Science
Year
2010
Tongue
French
Weight
177 KB
Volume
134
Category
Article
ISSN
0007-4497

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✦ Synopsis

Let (X, O X ) be a compact (reduced) complex space, bimeromorphic to a Kähler manifold. The singular cohomology groups H q (X, C) carry a mixed Hodge structure. In particular they carry a weight filtration W -l H q (X, C) (l = 0, . . . , q), and the graded quotients C) have a direct sum decomposition into holomorphic invariants as r+s=q-l ( W -l H q (X,C) W -l-1 H q (X,C) ) (r,s) . Here we investigate the relationships between the above invariants for r = 0 and the cohomology groups H q (X, ÕX ), where ÕX is the sheaf of weakly holomorphic functions on X. Moreover, according to the smooth case, we characterize the topological line bundles L on X such that the class of c 1 (L) in W 0 H 2 (X,C) W -1 H 2 (X,C) has pure type (1, 1).

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