KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

Jabbusch, K.

Lundman, Anders

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

2017 (English)In: The Michigan mathematical journal, ISSN 0026-2285, E-ISSN 1945-2365, Vol. 66, no 1, p. 21-35Article in journal (Refereed) Published

Abstract [en]

We study Gauss maps of order k, associated to a projective variety X embedded in projective space via a line bundle L. We show that if X is a smooth, complete complex variety and L is a k-jet spanned line bundle on X, with k ≥ 1, then the Gauss map of order k has finite fibers, unless X = Pn is embedded by the Veronese embedding of order k. In the case where X is a toric variety, we give a combinatorial description of the Gauss maps of order k, its image, and the general fibers.

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

Chachólski, Wojciech

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

Lundman, Anders

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

Ramanujam, Ryan

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

Öberg, Sebastian

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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2017 (English)In: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, Vol. 17, no 6, p. 1367-1406Article in journal (Refereed) Published

Abstract [en]

In this paper, we study multidimensional persistence modules (Carlsson and Zomorodian in Discrete Comput Geom 42(1):71–93, 2009; Lesnick in Found Comput Math 15(3):613–650, 2015) via what we call tame functors and noise systems. A noise system leads to a pseudometric topology on the category of tame functors. We show how this pseudometric can be used to identify persistent features of compact multidimensional persistence modules. To count such features, we introduce the feature counting invariant and prove that assigning this invariant to compact tame functors is a 1-Lipschitz operation. For one-dimensional persistence, we explain how, by choosing an appropriate noise system, the feature counting invariant identifies the same persistent features as the classical barcode construction.