Minimal bundles and fine moduli spaces

2009/03/13 by Georg Hein, Hein, Georg
Mathematics · #14D20 #14H40 #14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D20 #msc:14H40 #msc:14H60

paper · pdf · doi:10.48550/arxiv.0903.2330

10 pages

arxiv created 2009/03/13 · arxiv updated 2009/12/01

Abstract

We study sheaves E on a smooth projective curve X which are minimal with respect to the property that h⁰(E ⊗ L) >0 for all line bundles L of degree zero. We show that these sheaves define ample divisors D(E) on the Picard torus Pic(X). Next we classify all minimal sheaves of rank one and two. As an application we show that the moduli space parameterizing rank two bundles of odd degree can be obtained as a Quot scheme.

Related

• There are no exotic compact moduli of sheaves on a curve
• Sheaves on non-reduced curves in a projective surface
• Raynaud vector bundles
• Picard groups of the moduli spaces of semistable sheaves I
• Moduli of Very Ample Line Bundles