Bounded sets of sheaves on relative analytic spaces
Annales Henri Lebesgue, Volume 4 (2021), pp. 1531-1563.

Metadata

Keywordsbounded sets of coherent sheaves, relative analytic space, Douady space, Harder-Narasimhan filtration

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.


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