A lower bound for the degree of certain plane curves with prescribed singularities.

It is shown that the degree of a projective plane curve through r generic points with multiplicity m is strictly greater than root rm provided one of the following two conditions is satisfied r is a perfect square greater or equal to ten or r is greater than (8m(m + 1)/(4m - 1))(2) This result is part of a conjecture of Nagata, and the first case was already known to Nagata himself.