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arXiv · 1703.07344

Effective non-vanishing for Fano weighted complete intersections

Marco Pizzato·Taro Sano·Luca Tasin
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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.

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Marco Pizzato, Taro Sano, Luca Tasin. 2017-10-10. Effective non-vanishing for Fano weighted complete intersections. https://doi.org/10.2140/ant.2017.11.2369

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