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1.
Let
be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of
is provided when
is nef but not big, and when a suitable positive multiple of
defines a morphism X → B with connected fibers onto a smooth projective curve B, where KX is the canonical bundle of X. As an application, the case where the genus of B is positive and
has a global section whose zero locus is a smooth hyperelliptic curve of genus ≧ 2 is investigated, and our previous result
is improved for threefolds.
Received: 27 January 2005; revised: 26 March 2005 相似文献
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Francesco Malaspina 《Annali di Matematica Pura ed Applicata》2009,188(3):455-465
In this paper we give the classification of rank 3 vector bundles without “inner” cohomology on a quadric hypersurface (n > 3) by studying the associated monads.
相似文献
5.
Let X be a Fano 3-fold of the first kind with index 2. In this paper, we characterize the chern classes of rank 2 stable vector bundles on X and we find a bound for the least twist of a rank 2 reflexive sheaf on X which has a global section. 相似文献
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Robin Hartshorne 《Mathematische Annalen》1978,238(3):229-280
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E. Ballico R. M. Miró -Roig 《Proceedings of the American Mathematical Society》1999,127(9):2557-2560
Fix a smooth projective 3-fold , , with ample, and . Assume the existence of integers with such that is numerically equivalent to . Let be the moduli scheme of -stable rank 2 vector bundles, , on with and . Let be the number ofits irreducible components. Then .
8.
Laura Costa 《manuscripta mathematica》1999,100(3):335-349
Let be a ruled Fano 3-fold. The goal of this paper is to compute the dimension, prove the irreducibility and smoothness and describe
the structure of the moduli space M
L
(2;c
1,c
2) of L-stable, rank 2 vector bundles E on X with certain Chern classes and for a suitable polarization L closely related to c
2. More precisely, we will cover the study of some moduli spaces M
L
(2;c
1,c
2) such that the generic point is given as a non-trivial extension of line bundles. This work nicely reflects the general philosophy that moduli spaces
inherits a lot of geometrical properties of the underlying variety.
Received: 16 February 1999 / Revised version: 2 July 1999 相似文献
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Wojciech Kucharz 《Archiv der Mathematik》2016,107(3):239-249
We investigate vector bundles on real algebraic varieties. Our goal is to construct rank 2 real and complex stratified-algebraic vector bundles with prescribed Stiefel–Whitney and Chern classes, respectively. We obtain a partial solution of this problem and present two applications. 相似文献
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Lars Allermann 《Arkiv f?r Matematik》2012,50(2):237-258
We introduce tropical vector bundles, morphisms and rational sections of these bundles and define the pull-back of a tropical vector bundle and of a rational section along a morphism. Most of the definitions presented here for tropical vector bundles will be contained in Torchiani, C., Line Bundles on Tropical Varieties, Diploma thesis, Technische Universität Kaiserslautern, Kaiserslautern, 2010, for the case of line bundles. Afterwards we use the bounded rational sections of a tropical vector bundle to define the Chern classes of this bundle and prove some basic properties of Chern classes. Finally we give a complete classification of all vector bundles on an elliptic curve up to isomorphisms. 相似文献
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The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectively. Our argument leads to sufficient and necessary conditions for the existence of both kinds of bundles. The conclusion is very interesting because of its contradiction to the conjectured dimension formula of stable bundles. Finally, we give a preliminary classification of ω3^2,4 and a complete discussion on the structure of ω3^3,2/3g+2. 相似文献
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