Maximal Subsheaves of Torsion-Free Sheaves on Nodal Curves |
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Authors: | Bhosle Usha N. |
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Affiliation: | School of Mathematics, Tata Institute of Fundamental Research Homi Bhabha Road, Mumbai 4000005, India usha{at}math.tifr.res.in |
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Abstract: | Let Y be a reduced irreducible projective curve of arithmeticgenus g 2 with at most ordinary nodes as singularities. Fora subsheaf F of rank r', degree d' of a torsion-free sheaf Eof rank r, degree d, let s(E,F) = r'd-rd'. Define sr'(E) = mins(E,F), where the minimum is taken over all subsheaves of Eof rank r'. For a fixed r', sr' defines a stratification ofthe moduli space U(r,d) of stable torsion-free sheaves of rankr, degree d by locally closed subsets Ur',s. We study the nonemptinessand dimensions of the strata. We show that the general elementin each nonempty stratum is a vector bundle and it has onlyfinitely many (respectively unique) maximal subsheaves of rankr' for s r'(r-r')(g 1) (respectively s < r'(r-r')(g 1)). We prove that the tensor product of two generalstable vector bundles on an irreducible nodal curve Y is nonspecial. |
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