IJPAM: Volume 50, No. 1 (2009)

ON THE SCROLLAR INVARIANTS OF A NATURAL
PENCIL ON A PARTIAL NORMALIZATION OF
CERTAIN REDUCIBLE CURVES IN $\mathbb {P}^1\times \mathbb {P}^1$

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Here we prove that the scrollar invariants of a natural pencil on a partial normalization of certain reducible curves in $\mathbb {P}^1\times \mathbb {P}^1$ are as balanced as possible. We also prove that the pencil satisfies Caporaso's Basic Inequality for line bundles on semistable curves.

Received: December 20, 2008

AMS Subject Classification: 14H20, 14H51

Key Words and Phrases: tscrollar invariants, reducibble curve, curve in a quadric, quadric surface

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 1