HIGHER RANK INNER PRODUCTS, VORONOI TILINGS AND METRIC DEGENERATIONS OF TORI

Omid Amini; Noema Nicolussi

doi:10.5802/ahl.257

HIGHER RANK INNER PRODUCTS, VORONOI TILINGS AND METRIC DEGENERATIONS OF TORI

Omid Amini
, Noema Nicolussi

Laboratoire de Mathématiques d'Orsay
Department of Mathematics
University of Innsbruck

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a multi-scale generalization of the notion of scalar product on real and complex vector spaces and study the corresponding Voronoi tilings. This framework allows to analyze limiting metric structures involving several levels of convergence. In particular, we describe metric degenerations of polarized tori and Hausdorff limits of Voronoi tilings.

Translated title of the contribution	PRODUITS SCALAIRES MULTI-ÉCHELLES, DIAGRAMMES DE VORONOI ET DÉGÉNÉRESCENCES MÉTRIQUES DE TORES
Original language	English
Pages (from-to)	1109-1188
Number of pages	80
Journal	Annales Henri Lebesgue
Volume	8
DOIs	https://doi.org/10.5802/ahl.257
Publication status	Published - 1 Jan 2025
Externally published	Yes

Keywords

Voronoi tilings
asymptotic polyhedral geometry
higher rank inner products
higher rank tropical geometry
metric collapse
multi-scale geometry

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10.5802/ahl.257

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AB - We introduce a multi-scale generalization of the notion of scalar product on real and complex vector spaces and study the corresponding Voronoi tilings. This framework allows to analyze limiting metric structures involving several levels of convergence. In particular, we describe metric degenerations of polarized tori and Hausdorff limits of Voronoi tilings.

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KW - asymptotic polyhedral geometry

KW - higher rank inner products

KW - higher rank tropical geometry

KW - metric collapse

KW - multi-scale geometry

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ER -

HIGHER RANK INNER PRODUCTS, VORONOI TILINGS AND METRIC DEGENERATIONS OF TORI

Abstract

Keywords

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