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The paper shows that, if F
is a nonsplit rank 2 reflexive sheaf on P3, then the knowledge of the numbers
dn = h2(F(n)) − h1(F(n)) gives an explicit algorithm to compute the Chern
classes c1, c2, c3 and the dimensions h0(F(n)), for all n (in particular the first
integer a such that the sheaf F(a) has some nonzero section). If the sheaf is a
vector bundle it is also proved that the knowledge of the numerical sequence
{h1(F(n))} together with the first Chern class gives all the information as
above. In some special cases, i.e. when h1(F(n))≠0 for at most three values
of n, an algorithm is also produced to compute the first Chern class from
the sequence {h1(F(n))}. Vector bundles with natural cohomology are also
discussed.
It must be remarked that, if one knows not only the dimensions h1(F(n)), for all
n, but also the whole structure of the Rao-module ⊕
H1(F(n)), then the
first Chern class c1 is uniquely determined (as it is shown in a paper by P.
Rao).
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