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MiS Preprint
2/2020

Vanishing Hessian, wild forms and their border VSP

Hang Huang, Mateusz Michałek and Emanuele Ventura

Abstract

We show that forms with vanishing Hessian and of minimal border rank are wild, i.e. their smoothable rank is strictly larger than their border rank. This discrepancy is caused by the difference between the limit of spans of a family of zero-dimensional schemes and the span of their flat limit. We exhibit an infinite series of wild forms of every degree d≥3 as well as an infinite series of wild cubics. Inspired by recent work on border apolarity of Buczyńska and Buczyński, we study the border varieties of sums of powers of these forms in the corresponding multigraded Hilbert scheme.

Received:
Jan 2, 2020
Published:
Jan 24, 2020
MSC Codes:
14C05, 15A69

Related publications

inJournal
2020 Journal Open Access
Hang Huang, Mateusz Michałek and Emanuele Ventura

Vanishing Hessian, wild forms and their border VSP

In: Mathematische Annalen, 378 (2020) 3/4, pp. 1505-1532