Bounds for stable bundles and degrees of Weierstrass schemes (original) (raw)
1992, Mathematische Annalen
AI-generated Abstract
This paper addresses the stability of vector bundles on projective varieties, extending results from curves to higher dimensions. It establishes bounds on the degree of zero schemes associated with sections of semistable vector bundles through polynomial type functions in Chern classes, which allows the authors to derive upper bounds for the degrees of Weierstrass loci on varieties of general type. The main results are summarized in several theorems that contribute to understanding the geometry of Cohen-Macaulay varieties.
Related papers
Varieties of small degree with respect to codimension and ample vector bundles
Journal of the Mathematical Society of Japan, 2008
Let E be an ample vector bundle on a projective manifold X, with a section vanishing on a smooth subvariety Z of the expected dimension, and let H be an ample line bundle on X inducing a very ample ample line bundle H Z on Z. Triplets (X, E , H) as above are classified assuming that Z, embedded by |H Z |, is a variety of small degree with respect to codimension.
On the canonical degrees of curves in varieties of general type
Geometric and Functional Analysis, 2012
In this paper, we work in the framework of complex analytic varieties; without contrary mention, varieties are assumed to be irreducible (and reduced). If C is a projective curve, we let g C be its geometric genus (namely, the genus of its desingularization) and χ(C) = 2 − 2g C its geometric Euler characteristic; we also write deg C L for the degree of a line bundle L on C.
A criterion for ample vector bundles over a curve in positive characteristic
Bulletin des Sciences Mathématiques, 2005
Let X be a smooth projective curve defined over an algebraically closed field of positive characteristic. We give a necessary and sufficient condition for a vector bundle over X to be ample. This generalizes a criterion given by Lange in [Math. Ann. 238 (1978) 193-202] for a rank two vector bundle over X to be ample.
On semistable vector bundles over curves
Comptes Rendus Mathematique, 2008
Let X be a geometrically irreducible smooth projective curve defined over a field k, and let E be a semistable vector bundle on X. E is semistable if and only if there is a vector bundle F on X such that H i (X, F ⊗ E) = 0 for all i. We give an explicit bound for the rank of F , using a result of Popa for the case that k is algebraically closed.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.