Hilbert scheme and the structure of Aln P E

n-very ampleness, embeddings of the Hilbert scheme and the structure of Aln P(E)) 

Let AT be a projective scheme over an algebraically closed field k. In [Beltrametti-Sommese (1)] the following definition was made  

Definition 4.1.1. Let be an invertible sheaf on X. For every subscheme Z C X we study the restriction map 

Now we want to generalize this result to a relative situation. Let T be a reduced projective variety and X a projective scheme over T. Let 7r X — T be the projection. 

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