Journal article
A moment theoretic approach to estimate the cardinality of certain algebraic varieties
New York journal of mathematics, Vol.28, pp.357-366
01/01/2022
Abstract
For n is an element of N, we consider the algebraic variety V obtained by intersecting n+ 1 algebraic curves of degree n in R-2, when the leading terms of the associated bivariate polynomials are all different. We provide a new proof, based on the Flat Extension Theorem from the theory of truncated moment problems, that the cardinality of V cannot exceed ((2) (n+1)). In some instances, 2 this provides a slightly better estimate than the one given by Bezout's Theorem. Our main result contributes to the growing literature on the interplay between linear algebra, operator theory, and real algebraic geometry.
Details
- Title: Subtitle
- A moment theoretic approach to estimate the cardinality of certain algebraic varieties
- Creators
- Raul E Curto - Univ Iowa, Dept Math, Iowa City, IA 52242 USASeonguk Yoo - Gyeongsang Natl Univ, Dept Math Educ & Rins, Jinju 52828, South Korea
- Resource Type
- Journal article
- Publication Details
- New York journal of mathematics, Vol.28, pp.357-366
- Publisher
- ELECTRONIC JOURNALS PROJECT
- ISSN
- 1076-9803
- eISSN
- 1076-9803
- Number of pages
- 10
- Grant note
- NRF-2020R1F1A1A01070552 / Basic Science Research Program through the National Research Foundation of Korea - Ministry of Education
- Language
- English
- Date published
- 01/01/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984240879802771
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