Spaces of Holomorphic Maps with Bounded Multiplicity

Author: Yamaguchi K.

Source: Quarterly Journal of Mathematics, Volume 52, Number 2, 1 July 2001 , pp. 249-259(11)

Publisher: Oxford University Press

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Abstract:

Let Hol_d^* (S², CP^n-1) be the space consisting of all basepoint preserving holomorphic maps f : S² rarr

CP^n-1 of degree d. Then it is homeomorphic to the n-tuples (p₁(z), …, p_n(z)) isin

C[z]ⁿ of monic polynomials of degree d with no common root. Segal proved that it is a finite-dimensional model of OHgr

² CP^n-1. In this paper, we consider a certain subspace of it defined using the concept of multiplicity of roots, and we prove that it is also a finite-dimensional model of certain double loop space.

Document Type: Original article

Affiliations: 1: University of Electro-Communications, Chofu, Tokyo 182-8585, Japan. E-mail: kohhei@im.uec.ac.jp

Publication date: 2001-07-01

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The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. Areas such as algebra, differential geometry, and global analysis receive particular emphasis. However the journal avoids specialization.