English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We show a few basic results about moduli spaces of semistable modules overLie algebroids. The first result shows that such moduli spaces exist forrelative projective morphisms of noetherian schemes, removing some earlierconstraints. The second result proves general separatedness Langton typetheorem for such moduli spaces. More precisely, we prove S-completness of somemoduli stacks of semistable modules. In some special cases this resultidentifies closed points of the moduli space of Gieseker semistable sheaves ona projective scheme and of the Donaldson--Uhlenbeck compactification of themoduli space of slope stable locally free sheaves on a smooth projectivesurface. The last result generalizes properness of Hitchin's morphism and itshows properness of so called Hodge-Hitchin morphism defined in positivecharacteristic on the moduli space of Gieseker semistable integrablet-connections in terms of the p-curvature morphism. This last result was provenin the curve case by de Cataldo and Zhang using completely different methods.

Moduli spaces of semistable modules over Lie algebroids