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Journal Article

Effective nonvanishing for Fano weighted complete intersections

MPS-Authors
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Sano,  Taro
Max Planck Institute for Mathematics, Max Planck Society;

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Tasin,  Luca
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.2140/ant.2017.11.2369
(Publisher version)

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Fulltext (public)

arXiv:1703.07344.pdf
(Preprint), 328KB

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Citation

Pizzato, M., Sano, T., & Tasin, L. (2017). Effective nonvanishing for Fano weighted complete intersections. Algebra & Number Theory, 11(10), 2369-2395. doi:10.2140/ant.2017.11.2369.


Cite as: https://hdl.handle.net/21.11116/0000-0004-8ECB-8
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.