Effective nonvanishing for Fano weighted complete intersections

Pizzato, Marco; Sano, Taro; Tasin, Luca

doi:10.2140/ant.2017.11.2369

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Effective nonvanishing for Fano weighted complete intersections

Marco Pizzato, Taro Sano and Luca Tasin

Vol. 11 (2017), No. 10, 2369–2395

DOI: 10.2140/ant.2017.11.2369

Abstract

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.

Keywords

weighted complete intersections, nonvanishing, Ambro–Kawamata conjecture

Mathematical Subject Classification 2010

Primary: 14M10

Secondary: 11D04, 14J45

Milestones

Received: 29 March 2017

Revised: 28 July 2017

Accepted: 1 September 2017

Published: 31 December 2017

Authors

Marco Pizzato
I-39100 Bolzano Italy

Taro Sano
Department of Mathematics, Graduate School of Science Kobe University Kobe Japan

Luca Tasin
Dipartimento di Matematica e Fisica Roma Tre University Rome Italy

Vol. 11, No. 10, 2017