Generically nonreduced components of Hilbert schemes on fourfolds

Abstract

We exhibit generically nonreduced components of the Hilbert scheme of at least $21$ points on a smooth variety of dimension at least four. The result was announced in~[Jelisiejew__open_problems] and answers a question~[Problem~3.8, AIMPL]. The method is similar to the one of~[\S6, Jelisiejew-Šivic].

arXiv commentComments welcome! To appear in a special volume of Rendiconti del seminario matematico di Torino dedicated to Gianfranco Casnat