On the Harder-Narasimhan Filtration for Coherent Sheaves on P2: I

Let E be a torsion-free sheaf on P2. We give an effective method which uses the Hilbert function of E to construct a weak version of the Harder-Narasimhan filtration of a torsion-free sheaf on P2 subject only to the condition that E be sufficiently general among sheaves with that Hilbert function. T...

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Bibliographic Details
Main Author Walter, Charles H
Format Journal Article
LanguageEnglish
Published 20.12.1993
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DOI10.48550/arxiv.alg-geom/9312010

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Summary:Let E be a torsion-free sheaf on P2. We give an effective method which uses the Hilbert function of E to construct a weak version of the Harder-Narasimhan filtration of a torsion-free sheaf on P2 subject only to the condition that E be sufficiently general among sheaves with that Hilbert function. This algorithm uses on a generalization of Davis' decomposition lemma to higher rank.
DOI:10.48550/arxiv.alg-geom/9312010