Slopes of Vector Bundles on Projective Curves and Applications to Tight Closure Problems
نویسنده
چکیده
We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from below for the tight closure of a homogeneous R+-primary ideal in a two-dimensional normal standard-graded algebra R in terms of the minimal and the maximal slope of the sheaf of relations for some ideal generators. If moreover this sheaf of relations is semistable, then both degree estimates coincide and we get a vanishing type theorem.
منابع مشابه
1 1 Ju l 2 00 3 The Theory of Tight Closure from the Viewpoint of Vector Bundles
Contents Introduction 3 1. Foundations 13 1.1. A survey about the theory of tight closure 13 1.2. Solid closure and forcing algebras 23 1.3. Cohomological dimension 25 1.4. Vector bundles, locally free sheaves and projective bundles 28 2. Geometric interpretation of tight closure via bundles 30 2.1. Relation bundles 30 2.2. Affine-linear bundles arising from forcing algebras 32 2.3. Cohomology ...
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