(t, ℓ)-STABILITY AND COHERENT SYSTEMS

Abstract

Let X be a non-singular irreducible complex projective curve of genus g ≥ 2. The concept of stability of coherent systems over X depends on a positive real parameter α, given then a (finite) family of moduli spaces of coherent systems. We use (t, ℓ)-stability to prove the existence of coherent systems over X that are α-stable for all allowed α > 0.

Higher rank Brill—Noether theory and coherent systems open questions

“…When is U s (n, d, k) (U (n, d, k)) non-empty? Papers which address this question directly include [20,26,27,24,23]. When C is general and k = n + 1, the problem is related to Butler's Conjecture and is completely solved for U s (n, d, n + 1) and solved in most cases for U (n, d, n + 1) [13].…”