Sur la lissit\'e du sch\'ema Quot ponctuel embo\^it\'e

TL;DR

This paper characterizes the smoothness of nested Quot schemes of points on smooth varieties, extending Cheah's classification of smooth nested Hilbert schemes to a broader context.

Contribution

It provides a new criterion for smoothness of nested Quot schemes, generalizing previous results on Hilbert schemes.

Findings

Established conditions for smoothness of nested Quot schemes.

Extended Cheah's classification to more general Quot schemes.

Provided a geometric framework for understanding nested Quot schemes.

Abstract

In this paper we characterise the smoothness of the nested Quot scheme of points of a smooth variety, namely the moduli space parametrising flags of $0$-dimensional quotients of a fixed locally free sheaf. Our results extend Cheah's classification of smooth nested Hilbert schemes. -- Dans cet article on caract\'erise la lissit\'e du sch\'ema Quot ponctuel embo\^it\'e d'une vari\'et\'e lisse, c'est-\`a-dire l'espace de modules param\'etrant les drapeaux de quotients de dimension $0$ d'un faisceau localement libre fix\'e. Nos r\'esultats \'etendent la classification de Cheah concernant les sch\'emas de Hilbert ponctuels embo\^it\'es.