Geodesic
Vanishing of sections of vector bundles on 0-dimensional schemes
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 403-411.

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Here we give conditions and examples for the surjectivity or injectivity of the restriction map $H^0(X,F)\rightarrow H^0(Z,F\,|\, Z)$, where $X$ is a projective variety, $F$ is a vector bundle on $X$ and $Z$ is a ``general'' $0$-dimensional subscheme of $X$, $Z$ union of general ``fat points''.
Classification : 14F05, 14F17, 14J60, 14M05
Keywords: zero-dimensional scheme; cohomology; vector bundle; fat point 
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     title = {Vanishing of sections of vector bundles on 0-dimensional schemes},
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Ballico, E. Vanishing of sections of vector bundles on 0-dimensional schemes. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 403-411. http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a0/