Stable extensions by line bundles
Abstract
Let C be an algebraic curve of genus g. Consider extensions E of a vector bundle F'' of rank n'' by a vector bundle F' of rank n'. The following statement was conjectured by Lange: If 0<n'deg F''-n''degF' n'n''(g-1), then there exist extensions like this with E stable. We prove this result for the generic curve when F' is a line bundle. Our method uses a degeneration argument to a reducible curve.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.