On direct images of pluricanonical bundles

Popa, Mihnea; Schnell, Christian

doi:10.2140/ant.2014.8.2273

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On direct images of pluricanonical bundles

Mihnea Popa and Christian Schnell

Vol. 8 (2014), No. 9, 2273–2295

DOI: 10.2140/ant.2014.8.2273

Abstract

We show that techniques inspired by Kollár and Viehweg’s study of weak positivity, combined with vanishing for log-canonical pairs, lead to new generation and vanishing results for direct images of pluricanonical bundles. We formulate the strongest such results as Fujita conjecture-type statements, which are then shown to govern a range of fundamental properties of direct images of pluricanonical and pluriadjoint line bundles, like effective vanishing theorems, weak positivity, or generic vanishing.

Keywords

pluricanonical bundles, vanishing theorems, effective results

Mathematical Subject Classification 2010

Primary: 14F17

Secondary: 14E30, 14F05

Milestones

Received: 22 June 2014

Revised: 29 September 2014

Accepted: 7 November 2014

Published: 28 December 2014

Authors

Mihnea Popa
Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, IL 60208 United States

Christian Schnell
Department of Mathematics Stony Brook University Stony Brook, NY 11794 United States

Vol. 8, No. 9, 2014