Effective non-vanishing for Fano weighted complete intersections
Algebraic Geometry
2018-03-16 v2 Number Theory
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.
Cite
@article{arxiv.1703.07344,
title = {Effective non-vanishing for Fano weighted complete intersections},
author = {Marco Pizzato and Taro Sano and Luca Tasin},
journal= {arXiv preprint arXiv:1703.07344},
year = {2018}
}
Comments
27 pages. Revised version to appear in Algebra and Number Theory