Abstract
In this paper we address the classification of rank 2 vector bundles \(E,\) over \({\mathbb {P}}^{2}(\mathbb {C}),\) such that the zero locus of a general section of \(E\) is a set of distinct points in general position. We also discuss the existence of smooth threefolds \(X={\mathbb {P}}(E),\) arising from such bundles.
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Acknowledgments
The authors wish to thank: one of the referees for having pointed out a mistake in the first version of the paper and for the suggestion to take into account also the point of view of moduli in the study of ZGP bundles; G. Bini and P. Stellari for helpful discussions on the topic of moduli.
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A. Alzati and A. Tortora are members of CNR–GNSAGA (Italy).
During the preparation of this paper the authors were partially supported by National Research Project “Geometria sulle varietà algebriche COFIN 2010” of MIUR, Italy.
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Alzati, A., Tortora, A. Rank 2 vector bundles over \({\mathbb {P}}^{2}(\mathbb {C})\) whose sections vanish on points in general position. Rev Mat Complut 28, 623–654 (2015). https://doi.org/10.1007/s13163-015-0173-y
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DOI: https://doi.org/10.1007/s13163-015-0173-y