S\'eparation et propri\'et\'e de Deligne-Mumford des champs de modules d'intersections compl\`etes lisses

TL;DR

This paper proves that the moduli stacks of smooth complete intersections in projective space, polarized by O(1), are separated and Deligne-Mumford, with some exceptions such as quadrics.

Contribution

It establishes the separatedness and Deligne-Mumford property of these moduli stacks, extending understanding of their geometric structure.

Findings

Moduli stacks are separated except for quadrics.

Moduli stacks are Deligne-Mumford except for a few cases.

Provides conditions under which these stacks have desired properties.

Abstract

We show that the moduli stacks of smooth complete intersections in P^N polarized by O(1) are separated (except for quadrics) and Deligne-Mumford (apart from a few exceptions). ----- On montre que les champs de modules d'intersections completes lisses dans P^N polarisees par O(1) sont separes (sauf dans le cas des quadriques) et de Deligne-Mumford (sauf pour quelques exceptions).