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2017 Effective nonvanishing for Fano weighted complete intersections
Marco Pizzato, Taro Sano, Luca Tasin
Algebra Number Theory 11(10): 2369-2395 (2017). DOI: 10.2140/ant.2017.11.2369


We show that the Ambro–Kawamata nonvanishing conjecture holds true for a quasismooth 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 the Ambro–Kawamata conjecture for any quasismooth weighted hypersurface. We also verify Fujita’s freeness conjecture for a Gorenstein quasismooth weighted hypersurface.

For the proofs, we introduce the arithmetic notion of regular pairs and highlight some interesting connections with the Frobenius coin problem.


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Marco Pizzato. Taro Sano. Luca Tasin. "Effective nonvanishing for Fano weighted complete intersections." Algebra Number Theory 11 (10) 2369 - 2395, 2017.


Received: 29 March 2017; Revised: 28 July 2017; Accepted: 1 September 2017; Published: 2017
First available in Project Euclid: 1 February 2018

zbMATH: 06825454
MathSciNet: MR3744360
Digital Object Identifier: 10.2140/ant.2017.11.2369

Primary: 14M10
Secondary: 11D04 , 14J45

Keywords: Ambro–Kawamata conjecture , nonvanishing , weighted complete intersections

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.11 • No. 10 • 2017
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