Bounded sets of sheaves on relative analytic spaces

Toma, Matei

Annales Henri Lebesgue, Tome 4 (2021), pp. 1531-1563.

Nous étendons au cas relatif et pas nécessairement lisse les résultats précédemment obtenus sur les ensembles limités de faisceaux cohérents sur une variété kählérienne compacte. Ce contexte élargi nous permet de démontrer des énoncés de propreté pour l’espace de Douady relatif ainsi que des résultats liés à la semi-stabilité des faisceaux cohérents, comme l’existence des filtrations de Harder–Narasimhan relatives.

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.

Classification : 32J99, 14C05
Mots clés : bounded sets of coherent sheaves, relative analytic space, Douady space, Harder-Narasimhan filtration

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