A criterion for ample vector bundles over a curve in positive characteristic
نویسندگان
چکیده
منابع مشابه
A Generalization of Curve Genus for Ample Vector Bundles, I
A new genus g = g(X, E) is defined for the pairs (X, E) that consist of n-dimensional compact complex manifolds X and ample vector bundles E of rank r less than n on X. In case r = n − 1, g is equal to curve genus. Above pairs (X,E) with g less than two are classified. For spanned E it is shown that g is greater than or equal to the irregularity of X, and its equality condition is given.
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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 X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli space of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 with determinant equal to a theta characteristic whose Frobenius pull-back is not sta...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2005
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2004.12.002