Abstract: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''.
Keywords: zero-dimensional scheme, cohomology, vector bundle, fat point
AMS Subject Classification: 14J60, 14F05, 14F17