Bounded sets of sheaves on relative analytic spaces

Abstract

We extend previous results on boundedness of sets of coherent sheaves on a compact Kähler manifold to the relative and not necessarily smooth case. This enlarged context allows us to prove properness properties of the relative Douady space as well as results related to semistability of sheaves such as the existence of relative Harder-Narasimhan filtrations.

v2: Corollary 6.9 added; v3: changed title; published version

References in corpus (3)

• A continuity theorem for families of sheaves on complex surfaces
• Subharmonicity of direct images and applications
• Properness criteria for families of coherent analytic sheaves

Cited by in corpus (2)

• On the $4$-dimensional minimal model program for Kähler varieties
• Moduli spaces of slope-semistable sheaves with reflexive Seshadri graduations