Stable extensions by line bundles

Abstract

Let C be an algebraic curve of genus g. Consider extensions E of a vector bundle F&#39;&#39; of rank n&#39;&#39; by a vector bundle F&#39; of rank n&#39;. The following statement was conjectured by Lange: If 0<n&#39;deg F&#39;&#39;-n&#39;&#39;degF&#39;\le n&#39;n&#39;&#39;(g-1), then there exist extensions like this with E stable. We prove this result for the generic curve when F&#39; is a line bundle. Our method uses a degeneration argument to a reducible curve.