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MiS Preprint
91/2018

The rough Veronese variety

Francesco Galuppi

Abstract

We study signature tensors of paths from an algebraic geometric viewpoint. The signatures of a given class of paths parametrize a variety inside the space of tensors, and these signature varieties provide both new tools to investigate paths and new challenging questions about their behavior. This paper focuses on signatures of rough paths. Their signature variety shows surprising analogies with the Veronese variety, and our aim is to prove that this so-called Rough Veronese is toric. The same holds for the universal variety. Answering a question of Amendola, Friz and Sturmfels, we show that the ideal of the universal variety does not need to be generated by quadrics.

Received:
Oct 19, 2018
Published:
Oct 23, 2018
MSC Codes:
14Q15, 14M25, 60H99
Keywords:
signature tensor, rough path, Lyndon words

Related publications

inJournal
2019 Repository Open Access
Francesco Galuppi

The rough Veronese variety

In: Linear algebra and its applications, 583 (2019), pp. 282-299