IJPAM: Volume 55, No. 1 (2009)

LOW DEGREE SPANNED SHEAVES WITH PURE
RANK $1$ ON REDUCIBLE CURVES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Let $X$ be a reduced projective curve such that each point of $X$ lying on at least two irreducible components of $X$ is an ordinary node of $X$. Here we describe all spanned torsion free sheaves on $X$ with pure rank $1$ and degree $1$ or $2$. The list depends on combinatorial properties of $X$ (e.g. the existence of a disconnecting node of $X$).

Received: July 5, 2009

AMS Subject Classification: 14H51, 14H20

Key Words and Phrases: stable curve, reducible curve, torsion free sheaf, spanned line bundle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 1