A conjecture of the bounding cohomology on a smooth projective surface X
asserts that there exists a positive constant cXβ such that h1(OXβ(C))β€cXβh0(OXβ(C)) for every prime divisor C on X. When
the Picard number Ο(X)=2, we prove that if the Kodaira dimension
ΞΊ(X)=ββ and X has a negative curve, then this conjecture holds
for X.Comment: 6 pages, Comments are welcome. arXiv admin note: text overlap with
arXiv:2007.1285