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''.
@article{119097, author = {Edoardo Ballico}, title = {Vanishing of sections of vector bundles on 0-dimensional schemes}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {40}, year = {1999}, pages = {403-411}, zbl = {1013.14006}, mrnumber = {1732494}, language = {en}, url = {http://dml.mathdoc.fr/item/119097} }
Ballico, Edoardo. Vanishing of sections of vector bundles on 0-dimensional schemes. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 403-411. http://gdmltest.u-ga.fr/item/119097/
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