Effective non-vanishing conjectures for projective threefolds

Amaël Broustet (1) , Andreas Hoering (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 IMJ - Institut de Mathématiques de Jussieu

Let X be a smooth projective threefold, and let A be an ample line bundle such that K_X+A is nef. We show that if K_X or -K_X is pseudoeffective, the adjoint bundle K_X+A has global sections. We also give a very short proof of the Beltrametti-Sommese conjecture in dimension three, recently proven by Fukuma: if A is an ample line bundle such that K_X+2A is nef, the adjoint bundle K_X+2A has global sections.

Domains: Algebraic Geometry [math.AG]

Amaël Broustet, Andreas Hoering. Effective non-vanishing conjectures for projective threefolds. 2008. ⟨hal-00356734⟩