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Fasci debolmente positivi su di uno spazio complesso

Vincenzo Ancona — 1973

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Let be a coherent sheaf over a compact reduced complex space X , L ( ) the linear fiber space associated with , S k ( ) the k-th symmetric power of . We show that if the zero-section of L ( ) is exceptional, then H r ( X , 𝒪 X S k ( ) ) = 0 for every coherent sheaf on X and for r 1 and sufficiently large k. Using this result, we deduce that, if moreover Supp = X , then X is a Moišezon space.

Families of differential forms on complex spaces

Vincenzo AnconaBernard Gaveau — 2003

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On every reduced complex space X we construct a family of complexes of soft sheaves Λ X ; each of them is a resolution of the constant sheaf X and induces the ordinary De Rham complex of differential forms on a dense open analytic subset of X . The construction is functorial (in a suitable sense). Moreover each of the above complexes can fully describe the mixed Hodge structure of Deligne on a compact algebraic variety.

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