You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Maximal Degree Subsheaves of Torsion Free Sheaves on Singular Projective Curves
Transactions of the American Mathematical Society
Vol. 353, No. 9 (Sep., 2001), pp. 3617-3627
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2693805
Page Count: 11
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
Fix integers r,k,g with r > k > 0 and g ≥ 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)) ≥ k(deg(E)) - k(r - k)g. We show that for every g ≥ 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)) ≥ deg(E) - g. We show the existence of torsion free sheaves on non-Gorenstein projective curves with other pathological properties.
Transactions of the American Mathematical Society © 2001 American Mathematical Society