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Regularity on abelian varieties II: Basic results on linear series and defining equations
Author(s):
Giuseppe
Pareschi;
Mihnea
Popa
Journal:
J. Algebraic Geom.
13
(2004),
167-193.
Posted:
August 21, 2003
Retrieve article in:
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Abstract |
References |
Additional information
Abstract:
We apply the theory of  -regularity developed by the authors [Regularity on abelian varieties, I, J. Amer. Math. Soc. 16 (2003), 285-302] to the study of linear series given by multiples of ample line bundles on abelian varieties. We define an invariant of a line bundle, called  -regularity index, which governs the higher order properties and (partly conjecturally) the defining equations of such embeddings. We prove a general result on the behavior of the defining equations and higher syzygies in embeddings given by multiples of ample bundles whose base locus has no fixed components, extending a conjecture of Lazarsfeld [proved in Syzygies of abelian varieties, J. Amer. Math. Soc. 13 (2000), 651-664]. This approach also unifies essentially all the previously known results in this area, and is based on Fourier-Mukai techniques rather than representations of theta groups.
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Additional Information:
Giuseppe
Pareschi
Affiliation:
Dipartamento di Matematica, Università di Roma, Tor Vergata, V.le della Ricerca Scientifica, I-00133 Roma, Italy
Email:
pareschi@mat.uniroma2.it
Mihnea
Popa
Affiliation:
Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
Email:
mpopa@math.harvard.edu
PII:
S 1056-3911(03)00345-X
Received by editor(s):
October 21, 2001
Posted:
August 21, 2003
Additional Notes:
The second author was partially supported by a Clay Mathematics Institute Liftoff Fellowship during the preparation of this paper.
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