Quelques espaces de modules d'intersections compl\`etes lisses qui sont quasi-projectifs

TL;DR

This paper proves that for certain degrees, the coarse moduli space of smooth complete intersections in projective space is quasi-projective, using geometric invariant theory.

Contribution

It demonstrates the quasi-projectivity of the moduli space for smooth complete intersections with specific degrees, advancing understanding in algebraic geometry.

Findings

Moduli space is quasi-projective for certain degrees.

Uses geometric invariant theory to establish results.

Provides conditions under which the moduli space is quasi-projective.

Abstract

For some values of the degrees of the equations, we show, using geometric invariant theory, that the coarse moduli space of smooth complete intersections in P^N is quasi-projective. ----- Pour certaines valeurs des degres des equations, on montre, a l'aide de theorie geometrique des invariants, que l'espace de modules grossier des intersections completes lisses dans P^N est quasi-projectif.