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''.
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 
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/
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     author = {Ballico, E.},
     title = {Vanishing of sections of vector bundles on 0-dimensional schemes},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {403--411},
     year = {1999},
     volume = {40},
     number = {3},
     mrnumber = {1732494},
     zbl = {1013.14006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1999_40_3_a0/}
}
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