Bounding cohomology on a smooth projective surface with Picard number 2. Issue 7 (18th June 2021)

• Record Type: Journal Article
• Authors: Li, Sichen
• Is Part Of: Communications in algebra. Volume 49:Issue 7(2021)
• Page Start: 3140
• Page End: 3144
• Publication Date: 2021-06-18
• Subjects: Bounded negativity conjecture -- bounding cohomology -- Picard number 2; Primary 14C20; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1888962
• Languages: English
• ISSNs: 0092-7872

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 h 1 ( O X ( C ) ) ≤ c X h 0 ( O X ( C ) ) for every prime divisor C on X . When the Picard number ρ ( X ) = 2, we prove that if either the Kodaira dimension κ ( X ) = 1 and X has a negative curve or X has two negative curves, then this conjecture holds for X .