Stability and deformations of generalised Picard sheaves

2018/12/23 by Biswas, I., Brambila-Paz, L., Newstead, P. E.
#14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.09732

Abstract

Let C be a smooth irreducible complex projective curve of genus g ≥ 2 and M the moduli space of stable vector bundles on C of rank n and degree d with gcd(n,d)=1. A generalised Picard sheaf is the direct image on M of the tensor product of a universal bundle on M× C by the pullback of a vector bundle E₀ on C. In this paper, we investigate the stability of generalised Picard sheaves and, in the case where these are locally free, their deformations. When g≥3, n≥2 (with some additional restrictions for g=3,4) and the rank and degree of E₀ are coprime, this leads to the construction of a fine moduli space for deformations of Picard bundles.

Related

• Deformations of the generalised Picard bundle
• Deformations of the Picard Bundle
• Stability of Picard sheaves for vector bundles on curves
• Stability of the Parabolic Picard Sheaf
• Picard groups of the moduli spaces of semistable sheaves I