IJPAM: Volume 29, No. 3 (2006)

HOLOMORPHIC TRIPLES ON SMOOTH ALGEBRAIC
CURVES AND $\alpha$-STABILITY

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $X$ be a smooth curve of genus $g \ge 2$. Here we study the $\alpha$-stability of a holomorphic triple $(E_2,E_1,\phi )$ on $X$ in the following cases:

(i) $E_2$ is a general stable bundle and $E_1$ is a general extension of a general stable bundle $E_3$ by $E_2$;

(ii) $E_1$ is a general stable bundle and $E_2$ is a maximal degree subbundle of $E_1$ for a prescribed rank.

Received: May 10, 2006

AMS Subject Classification: 14H60

Key Words and Phrases: holomorphic triples on curves, vector bundles on curves, stable vector bundles, general stable vector bundle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 29
Issue: 3