Effective non-vanishing for Fano weighted complete intersections

Abstract

We show that Ambro-Kawamata's non-vanishing conjecture holds true for a quasi-smooth WCI X which is Fano or Calabi-Yau, i.e. we prove that, if H is an ample Cartier divisor on X, then |H| is not empty. If X is smooth, we further show that the general element of |H| is smooth. We then verify Ambro-Kawamata's conjecture for any quasi-smooth weighted hypersurface. We also verify Fujita's freeness conjecture for a Gorenstein quasi-smooth weighted hypersurface. For the proofs, we introduce the arithmetic notion of regular pairs and enlighten some interesting connection with the Frobenius coin problem.

27 pages. Revised version to appear in Algebra and Number Theory

References in corpus (2)

• Bounds for smooth Fano weighted complete intersections
• Nef partitions for codimension 2 weighted complete intersections

Cited by in corpus (7)

• Bounds for smooth Fano weighted complete intersections
• Hodge level for weighted complete intersections
• Automorphisms of weighted complete intersections
• Nef partitions for codimension 2 weighted complete intersections
• The classification of smooth well-formed Fano weighted complete intersections
• Weighted Grassmannians and their explicit description
• Belyi's theorem for smooth complete intersections of general type in generalised Grassmannians and weighted projective spaces