Spaces of algebraic maps from real projective spaces to toric varieties

作者：KonowsKi Andrzej^*; Ohno Masahiro^*; Yamaguchi Kohhei^*

来源：Journal of the Mathematical Society of Japan, 2016, 68(2): 745-771.

DOI：10.2969/jmsj/06820745

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

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) -> infinity as D -> infinity. 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.

• 出版日期2016-4