Boundedness for sets of coherent analytic sheaves

Abstract: A boundedness notion for sets of isomorphism classes of coherent algebraic sheaves as well as a boundedness criterion were introduced by Grothendieck in his 1961 paper on the construction of the Hilbert scheme. In this talk we define boundedness for coherent analytic sheaves and present a boundedness criterion in a complex geometric context. We then show how these apply to prove properties related to Douady spaces or to semistability of coherent sheaves, such as the existence of relative Harder-Narasimhan filtrations.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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The livestream is on Zoom at : uqam.zoom.us/j/98999725241 (no password is needed).

The recorded talks can be found at CIRGET channel : www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA