A note on the postulation of maximal rank curves
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Let s be the lowest degree of a surface containing a maximal rank curve Y. We want to compare the dimension of the space of the surfaces of degree s containing Y with the dimension of the space of the surfaces of degree s+1. We apply the bound that we find for getting a bound for the third Chern class of a rank-two reflexive sheaf on Pk 3 with seminatural cohomology, thus answering to a conjecture proposed by R. Hartshorne.