Hausdorff approximations and volume of tubes of singular algebraic sets

We prove bounds for the volume of neighborhoods of algebraic sets, in the euclidean space or the sphere, in terms of the degree of the defining polynomials, the number of variables and the dimension of the algebraic set, without any smoothness assumption. This generalizes previous work of Lotz (Proc...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematische annalen Jg. 387; H. 1-2; S. 79 - 109
Hauptverfasser: Basu, Saugata, Lerario, Antonio
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2023
Springer Nature B.V
Schlagworte:
Algebra
Algorithms
Euclidean geometry
Geometry
Hyperspaces
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical analysis
Polynomials
Smoothness
Tubes
ISSN:0025-5831, 1432-1807
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We prove bounds for the volume of neighborhoods of algebraic sets, in the euclidean space or the sphere, in terms of the degree of the defining polynomials, the number of variables and the dimension of the algebraic set, without any smoothness assumption. This generalizes previous work of Lotz (Proc Am Math Soc 143(5):1875–1889, 2015) on smooth complete intersections in the euclidean space and of Bürgisser et al. (Math Comp 77(263):1559–1583, 2008) on hypersurfaces in the sphere, and gives a complete solution to Bürgisser and Cucker (Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol 349, Springer, Heidelberg, 2013, Problem 17).
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-022-02458-w