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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The stable reduction theorem of Deligne and Mumford --- The moduli space ofsmooth projective curves of genus $g$ is a quasi-projective algebraic variety,but is not projective. To understand its geometry, it may be crucial toconsider compactifications of this space. By allowing to parameterize as wellcurves with controlled singularities (the so called stable curves), Deligne andMumford constructed a projective compactification. The properness of thiscompactification translates into the stable reduction theorem that they prove,its projectivity is a later theorem of Knudsen and Mumford. This text is basedon the oral presentation and aims at introducing these objects.

Le th\'eor\`eme de r\'eduction stable de Deligne et Mumford