Abstract The following conjecture arose out of discussions between B. Harbourne, J. Roé, C. Cilberto and R. Miranda: for a smooth projective surface X there exists a positive constant cX… Click to show full abstract
Abstract The following conjecture arose out of discussions between B. Harbourne, J. Roé, C. Cilberto and R. Miranda: for a smooth projective surface X there exists a positive constant cX such that for every prime divisor C on X. When the Picard number we prove that if either the Kodaira dimension and X has a negative curve or X has two negative curves, then this conjecture holds for X.
               
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