P-Ample Bundles and Their Chern Classes

In [9], Hartshorne extended the concept of ampleness from line bundles to vector bundles. At that time, he conjectured that the appropriate Chern classes of an ample vector bundle were positive, and it was hoped that there would be some criterion for ampleness of vector bundles similar to Nakai’s cr...

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Bibliographic Details
Published inNagoya mathematical journal Vol. 43; pp. 91 - 116
Main Author Gieseker, David
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.01.1971
Duke University Press
Subjects
14L05
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Summary:In [9], Hartshorne extended the concept of ampleness from line bundles to vector bundles. At that time, he conjectured that the appropriate Chern classes of an ample vector bundle were positive, and it was hoped that there would be some criterion for ampleness of vector bundles similar to Nakai’s criterion for line bundles. In the same paper, Hartshorne also introduced the notion of p-ample when the ground field had characteristic p, proved that a p-ample bundle was ample and asked if the converse were true.
ISSN:0027-7630
2152-6842
DOI:10.1017/S0027763000014380