Vol. 8, No. 9, 2014

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
On direct images of pluricanonical bundles

Mihnea Popa and Christian Schnell

Vol. 8 (2014), No. 9, 2273–2295
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