IJPAM: Volume 54, No. 4 (2009)

ON THE EXISTENCE OF DEGREE $g$ SPANNED
RANK $1$ SHEAVES ON INTEGRAL CURVES
AND ON BINARY CURVES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $X$ be either an integral projective curve curve with only ordinary nodes or ordinary cusps (resp. a binary curve). Set $g:=p_a(X)$. Here we prove the existence on $X$ of degree $g$ spanned rank $1$ torsion free sheaves (resp. $\omega _X$-semistable line bundles).

Received: July 2, 2009

AMS Subject Classification: 14H51

Key Words and Phrases: binary curve, singular curve, spanned torsion free sheaf theory, binary curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 4