EUDML

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Sui fibrati analitici reali $E$ -principali. II. - Teoremi di classificazione

Vincenzo Ancona — 1976

Rendiconti del Seminario Matematico della Università di Padova

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

Same Applications of Beilinson's Theorem to Projective Spaces and Quadrics.

Giorgio Ottaviani; Vincenzo Ancona — 1991

Forum mathematicum

The Horrocks bundles of rank three on P5.

Giorgio Ottaviani; Vincenzo Ancona — 1995

Journal für die reine und angewandte Mathematik

Families of differential forms on complex spaces

Vincenzo Ancona; Bernard 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 $ℂ_{X}$ 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.