Journal of the Mathematical Society of Japan

Varieties of small degree with respect to codimension and ample vector bundles

Antonio LANTERI and Carla NOVELLI

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Abstract

Let  E   be an ample vector bundle on a projective manifold X , with a section vanishing on a smooth subvariety Z   of the expected dimension, and let H   be an ample line bundle on X   inducing a very ample ample line bundle H Z   on Z . Triplets (X,E,H) as above are classified assuming that Z , embedded by | H Z | , is a variety of small degree with respect to codimension.

Article information

Source
J. Math. Soc. Japan, Volume 60, Number 2 (2008), 341-361.

Dates
First available in Project Euclid: 30 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1212156654

Digital Object Identifier
doi:10.2969/jmsj/06020341

Mathematical Reviews number (MathSciNet)
MR2421980

Zentralblatt MATH identifier
1170.14030

Subjects
Primary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14C20: Divisors, linear systems, invertible sheaves 14J40: $n$-folds ($n > 4$) 14N30: Adjunction problems

Keywords
ample vector bundles special varieties $\Delta$-genus adjunction theory Fano manifolds classification

Citation

LANTERI, Antonio; NOVELLI, Carla. Varieties of small degree with respect to codimension and ample vector bundles. J. Math. Soc. Japan 60 (2008), no. 2, 341--361. doi:10.2969/jmsj/06020341. https://projecteuclid.org/euclid.jmsj/1212156654


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