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http://dx.doi.org/10.4134/JKMS.2009.46.3.589

CURVES AND VECTOR BUNDLES ON QUARTIC THREEFOLDS  

Arrondo, Enrique (DEPARTAMENTO DE ALGEBRA FACULTAD DE CIENCIAS MATEMATICAS UNIVERSIDAD COMPLUTENSE DE MADRID)
Madonna, Carlo G. (DEPARTAMENTO DE ALGEBRA FACULTAD DE CIENCIAS MATEMATICAS UNIVERSIDAD COMPLUTENSE DE MADRID)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.3, 2009 , pp. 589-607 More about this Journal
Abstract
In this paper we study arithmetically Cohen-Macaulay (ACM for short) vector bundles $\varepsilon$ of rank k $\geq$ 3 on hypersurfaces $X_r\;{\subset}\;{\mathbb{P}}^4$ of degree r $\geq$ 1. We consider here mainly the case of degree r = 4, which is the first unknown case in literature. Under some natural conditions for the bundle $\varepsilon$ we derive a list of possible Chern classes ($c_1$, $c_2$, $c_3$) which may arise in the cases of rank k = 3 and k = 4, when r = 4 and we give several examples.
Keywords
quartic threefold; ACM bundle; projectively normal curve;
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