Tight closure and projective bundles

2002/09/23 by Holger Brenner
Mathematics · #math.AC #math.AG #msc:14H60 #msc:14J26 #msc:13A35

paper · pdf

published as J. Algebra 265 (2003), 45-78. · 28 pages, to appear in Journal of Algebra

arxiv created 2002/09/23 · arxiv updated 2009/11/30

Abstract

We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning the tight closure of a primary ideal in a two-dimensional graded domain.

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• Slopes of vector bundles on projective curves and applications to tight closure problems
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