It is known that to every bundle on a surface we may assign three discrete invariants: the rank , and the first and second Chern classes, and . The author gives sufficient conditions on the invariants that guarantee that on a K3 surface with one-dimensional Picard group there exist stable bundles that realize the given invariants. Bibliography: 8 titles.
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Sergej Alekseevich Kuleshov (1991) studied this question.
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