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Lundman, Anders
Publications (2 of 2) Show all publications
Di Rocco, S., Jabbusch, K. & Lundman, A. (2017). A note on higher-order gauss maps. The Michigan mathematical journal, 66(1), 21-35
Open this publication in new window or tab >>A note on higher-order gauss maps
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.

Place, publisher, year, edition, pages
University of Michigan, 2017
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-207438 (URN)000399854800002 ()2-s2.0-85015345512 (Scopus ID)
Note

QC 20170523

Available from: 2017-05-23 Created: 2017-05-23 Last updated: 2017-05-24Bibliographically approved
Scolamiero, M., Chachólski, W., Lundman, A., Ramanujam, R. & Öberg, S. (2017). Multidimensional Persistence and Noise. Foundations of Computational Mathematics, 17(6), 1367-1406
Open this publication in new window or tab >>Multidimensional Persistence and Noise
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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.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2017
Keywords
Multidimensional persistence, Noise systems, Persistence modules, Stable invariants, Computational methods, Mathematical techniques, Functors, Persistent feature, Pseudo-metrices, Algebra
National Category
Algebra and Logic
Identifiers
urn:nbn:se:kth:diva-197199 (URN)10.1007/s10208-016-9323-y (DOI)000415739500001 ()2-s2.0-84976493395 (Scopus ID)
Note

QC 20161212

Available from: 2016-12-12 Created: 2016-11-30 Last updated: 2017-12-08Bibliographically approved
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