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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Maximal degree subsheaves of torsion free sheaves on singular projective curves


Author: E. Ballico
Journal: Trans. Amer. Math. Soc. 353 (2001), 3617-3627
MSC (2000): Primary 14H20, 14H60
Published electronically: April 18, 2001
MathSciNet review: 1837251
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Abstract:

Fix integers $r,k,g$ with $r>k>0$ and $g\ge 2$. Let $X$ be an integral projective curve with $g:=p_a(X)$ and $E$ a rank $r$ torsion free sheaf on $X$which is a flat limit of a family of locally free sheaves on $X$. Here we prove the existence of a rank $k$ subsheaf $A$ of $E$ such that $r(\deg(A))\ge k(\deg (E))-k(r-k)g$. We show that for every $g\ge 9$ there is an integral projective curve $X,X$ not Gorenstein, and a rank 2 torsion free sheaf $E$ on $X$ with no rank 1 subsheaf $A$ with $2(\deg (A))\ge \deg(E)-g$. We show the existence of torsion free sheaves on non-Gorenstein projective curves with other pathological properties.


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Additional Information

E. Ballico
Affiliation: Dipartimento di Matematicà, Università di Trento, 38050 Povo (TN) - Italy
Email: ballico@science.unitn.it

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02745-3
PII: S 0002-9947(01)02745-3
Received by editor(s): September 25, 1998
Published electronically: April 18, 2001
Article copyright: © Copyright 2001 American Mathematical Society