Open Access
April, 2016 Spaces of algebraic maps from real projective spaces to toric varieties
Andrzej KOZLOWSKI, Masahiro OHNO, Kohhei YAMAGUCHI
J. Math. Soc. Japan 68(2): 745-771 (April, 2016). DOI: 10.2969/jmsj/06820745


The problem of approximating the infinite dimensional space of all continuous maps from an algebraic variety $X$ to an algebraic variety $Y$ by finite dimensional spaces of algebraic maps arises in several areas of geometry and mathematical physics. An often considered formulation of the problem (sometimes called the Atiyah–Jones problem after [1]) is to determine a (preferably optimal) integer $n_D$ such that the inclusion from this finite dimensional algebraic space into the corresponding infinite dimensional one induces isomorphisms of homology (or homotopy) groups through dimension $n_D$, where $D$ denotes a tuple of integers called the “degree” of the algebraic maps and $n_D\to\infty$ as $D\to\infty$. In this paper we investigate this problem in the case when $X$ is a real projective space and $Y$ is a smooth compact toric variety.


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Andrzej KOZLOWSKI. Masahiro OHNO. Kohhei YAMAGUCHI. "Spaces of algebraic maps from real projective spaces to toric varieties." J. Math. Soc. Japan 68 (2) 745 - 771, April, 2016.


Published: April, 2016
First available in Project Euclid: 15 April 2016

zbMATH: 1353.55009
MathSciNet: MR3488144
Digital Object Identifier: 10.2969/jmsj/06820745

Primary: 55R80
Secondary: 14M25 , 55P10 , 55P35

Keywords: algebraic map , fan , homogenous coordinate , primitive element , rational polyhedral cone , simplicial resolution , toric variety , Vassiliev spectral sequence

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 2 • April, 2016
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