Vol. 5, No. 2, 2011

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Local positivity, multiplier ideals, and syzygies of abelian varieties

Robert Lazarsfeld, Giuseppe Pareschi and Mihnea Popa

Vol. 5 (2011), No. 2, 185–196
Abstract

We use the language of multiplier ideals in order to relate the syzygies of an abelian variety in a suitable embedding with the local positivity of the line bundle inducing that embedding. This extends to higher syzygies a result of Hwang and To on projective normality.

Keywords
Syzygies, abelian varieties, local positivity, multiplier ideals
Mathematical Subject Classification 2000
Primary: 14K05
Secondary: 14Q20, 14F17
Milestones
Received: 11 March 2010
Revised: 23 April 2010
Accepted: 22 May 2010
Published: 27 August 2011
Authors
Robert Lazarsfeld
Department of Mathematics
University of Michigan
Ann Arbor, MI 48109-1043
United States
http://www.math.lsa.umich.edu/~rlaz
Giuseppe Pareschi
Dipartimento di Matematica
Università di Roma, Tor Vergata
V.le Della Ricerca Scientifica
I-00133 Roma
Italy
http://www.mat.uniroma2.it/~pareschi
Mihnea Popa
Department of Mathematics
University of Illinois at Chicago
851 S. Morgan Street
Chicago, IL 60607
United States
http://www.math.uic.edu/~mpopa