THEORY OF LINE BUNDLES AND SMOOTH VARIETIES

We give a K-theoretic criterion for a quasi-projective variety to be smooth. If L is a line bundle corresponding to an ample invertible sheaf on X, it suffices that Kq(X) ≅ Kq(L) for all q ≤ dim(X) + 1.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2018-10, Vol.146 (10), p.4139-4150
Main Authors: HAESEMEYER, C., WEIBEL, C.
Format: Article
Language:English
Subjects:
A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS
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Summary:We give a K-theoretic criterion for a quasi-projective variety to be smooth. If L is a line bundle corresponding to an ample invertible sheaf on X, it suffices that Kq(X) ≅ Kq(L) for all q ≤ dim(X) + 1.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14112