previous :: next
Effective very ampleness for generalized theta divisors
Eduardo Esteves and Mihnea Popa
Source: Duke Math. J. Volume 123, Number 3
(2004), 429-444.
Abstract
Given a smooth projective curve X, we give effective very ampleness bounds for generalized theta divisors on the moduli spaces SUX(r,d) and UX(r,d) of semistable vector bundles of rank r and degree d on X with fixed, respectively, arbitrary, determinant.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1086957712
Digital Object Identifier: doi:10.1215/S0012-7094-04-12331-0
Mathematical Reviews number (MathSciNet): MR2068965
Zentralblatt MATH identifier: 02103762
References
L. Brambila-Paz, I. Grzegorczyk, and P. E. Newstead, Geography of Brill-Noether loci for small slopes, J. Algebraic Geom. 6 (1997), 645--669.
Mathematical Reviews (MathSciNet): MR1487229
S. Brivio and A. Verra, The theta divisor of $\SU_C(2,2d)^s$ is very ample if $C$ is not hyperelliptic, Duke Math. J. 82 (1996), 503--552.
Mathematical Reviews (MathSciNet): MR1387683
Digital Object Identifier: doi:10.1215/S0012-7094-96-08222-8
Project Euclid: euclid.dmj/1077245251
Zentralblatt MATH: 0876.14024
--. --. --. --., On the theta divisor of $\SU(2,1)$, Internat. J. Math. 10 (1999), 925--942.
Mathematical Reviews (MathSciNet): MR1739370
Digital Object Identifier: doi:10.1142/S0129167X99000409
Zentralblatt MATH: 1077.14536
R. Donagi and L. W. Tu, Theta functions for $\text\rm SL(n)$ versus $\text\rm GL(n)$, Math. Res. Lett. 1 (1994), 345--357.
Mathematical Reviews (MathSciNet): MR1302649
J.-M. Drezet and M. S. Narasimhan, Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques, Invent. Math. 97 (1989), 53--94.
Mathematical Reviews (MathSciNet): MR0999313
Digital Object Identifier: doi:10.1007/BF01850655
E. Esteves, Separation properties of theta functions, Duke Math. J. 98 (1999), 565--593.
Mathematical Reviews (MathSciNet): MR1695802
Digital Object Identifier: doi:10.1215/S0012-7094-99-09818-6
Project Euclid: euclid.dmj/1077228360
Zentralblatt MATH: 0983.14028
G. Faltings, Stable $G$-bundles and projective connections, J. Algebraic Geom. 2 (1993), 507--568.
Mathematical Reviews (MathSciNet): MR1211997
B. van Geemen and E. Izadi, The tangent space to the moduli space of vector bundles on a curve and the singular locus of the theta divisor of the Jacobian, J. Algebraic Geom. 10 (2001), 133--177.
Mathematical Reviews (MathSciNet): MR1795553
S. L. Kleiman, The transversality of a general translate, Compositio Math. 28 (1974), 287--297.
Mathematical Reviews (MathSciNet): MR0360616
H. Lange, Zur Klassifikation von Regelmannigfaltigkeiten, Math. Ann. 262 (1983), 447--459.
Mathematical Reviews (MathSciNet): MR0696517
Digital Object Identifier: doi:10.1007/BF01456060
Zentralblatt MATH: 0492.14003
G. Pareschi and M. Popa, Regularity on abelian varieties, I, J. Amer. Math. Soc. 16 (2003), 285--302.
Mathematical Reviews (MathSciNet): MR1949161
Digital Object Identifier: doi:10.1090/S0894-0347-02-00414-9
Zentralblatt MATH: 1022.14012
M. Popa, Dimension estimates for Hilbert schemes and effective base point freeness on moduli spaces of vector bundles on curves, Duke Math J. 107 (2001), 469--495.
Mathematical Reviews (MathSciNet): MR1828298
Digital Object Identifier: doi:10.1215/S0012-7094-01-10732-1
Project Euclid: euclid.dmj/1091737020
Zentralblatt MATH: 1064.14032
--. --. --. --., Verlinde bundles and generalized theta linear series, Trans. Amer. Math. Soc. 354 (2002), 1869--1898.
Mathematical Reviews (MathSciNet): MR1881021
Digital Object Identifier: doi:10.1090/S0002-9947-01-02923-3
JSTOR: links.jstor.org
Zentralblatt MATH: 0996.14015
M. Popa and M. Roth, Stable maps and Quot schemes, Invent. Math. 152 (2003), 625--663.
Mathematical Reviews (MathSciNet): MR1988296
Digital Object Identifier: doi:10.1007/s00222-002-0279-y
Zentralblatt MATH: 1024.14015
M. Teixidor i Bigas and L. W. Tu, ``Theta divisors for vector bundles'' in Curves, Jacobians, and Abelian Varieties (Amherst, Mass., 1990), Contemp. Math. 136, Amer. Math. Soc., Providence, 1992, 327--342.
Mathematical Reviews (MathSciNet): MR1188206
previous :: next
Duke Mathematical Journal
