On the cohomology of projective curves

Abstract

Let Y be an integral, nondegenerate curve in P n and let I Y be its ideal sheaf. In this paper, the authors give bounds on the dimension of the cohomology groups h i (I Y (t)) , t>0 , 1≤i≤2 , in terms of the degree, the arithmetic genus and the index of speciality of Y . The results of this paper are not really new but they put into evidence the interest of giving the list of all possible cohomologies