We apply the theory of M-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 M-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.

Pareschi, G., Popa, M. (2004). Regularity on abelian vaneties II: Basic results on linear series and defining equations. JOURNAL OF ALGEBRAIC GEOMETRY, 13(1), 167-193 [10.1090/S1056-3911-03-00345-X].

Regularity on abelian vaneties II: Basic results on linear series and defining equations

PARESCHI, GIUSEPPE;
2004-01-01

Abstract

We apply the theory of M-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 M-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.
2004
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
DERIVED CATEGORY; ABELIAN VARIETIES, FOURIER-MUKAI TRANFORM, DEFINING EQUATIONS, SYZYGIES
http://www.ams.org/journals/jag/2004-13-01/S1056-3911-03-00345-X/
Pareschi, G., Popa, M. (2004). Regularity on abelian vaneties II: Basic results on linear series and defining equations. JOURNAL OF ALGEBRAIC GEOMETRY, 13(1), 167-193 [10.1090/S1056-3911-03-00345-X].
Pareschi, G; Popa, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/31564
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