# Kristian Ranestad (UiO) - Bad limits in power sum varieties

The variety of sums of powers, VSP(F, r) of a homogeneous form F of rank r is the closure in the Hilbert scheme of apolar schemes of length r. A bad limit is a scheme in the closure that is not apolar to F. I will discuss examples of bad limits, including examples for quadrics found by Joachim Jelisiejew that contradicts earlier results on polar simplicies. This is report on work in progress with Jelisiejew and Schreyer and with Grzegorz and Michal Kapustka.

Published Oct. 7, 2022 7:35 AM
- Last modified Nov. 21, 2022 9:32 AM