Vector bundles on ample divisors
نویسندگان
چکیده
منابع مشابه
A Positivity Property of Ample Vector Bundles
Using Fujita-Griffiths method of computing metrics on Hodge bundles, we show that for every semi-ample vector bundle E on a compact complex manifold, and every positive integer k, the vector bundle SE ⊗ detE has a continuous metric with Griffiths semi-positive curvature. If E is ample, the metric can be made smooth and Griffiths positive.
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Since the seminal paper published by P.A. Griffiths in 1969 [7], a whole series of vanishing theorems have been established for the Dolbeault cohomology of ample vector bundles on smooth projective varieties, mainly due to the efforts of J. Le Potier, M. Schneider, A. Sommese, J-P. Demailly, L. Ein and R. Lazarsfeld, the author, and more recently W. Nahm [2, 5, 11, 15, 16, 18, 19, 21]. This abu...
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Let E be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of E is provided when KX+detE is nef but not big, and when a suitable positive multiple of KX+det E defines a morphism X → B with connected fibers onto a smooth projective curve B, where KX is the canonical bundle of X. As an application, the case where the genus...
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Let E be an ample rank r bundle on a smooth toric projective surface, S, whose topological Euler characteristic is e(S). In this article, we prove a number of surprisingly strong lower bounds for c1(E) and c2(E). First, we show Corollary (3.2), which says that, given S and E as above, if e(S) ≥ 5, then c1(E) ≥ r2e(S). Though simple, this is much stronger than the known lower bounds over not nec...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1981
ISSN: 0025-5645
DOI: 10.2969/jmsj/03330405