Spaces of polynomials with roots of bounded multiplicity

Abstract

Spaces of polynomials with roots of bounded multiplicity by M. A. G u e s t (Rochester, NY, and Tokyo), A. K o z l o w s k i (Toyama) and K. Y a m a g u c h i (Tokyo)

Spaces of Morphisms From a Projective Space to a Toric Variety

“…A very general conjecture on this subject is given in the paper of Cohen, Jones and Segal [3]. Several papers [12,17] give real versions of Segal's theorem (the first real version being due to Segal himself in [20]).…”

The homology of spaces of polynomials with roots of bounded multiplicity

“…Remarks 2.3 (i) It is proved by Guest, Kozlowski and Yamaguchi in [8] that the (modified) jet map P 0 k,n → Rat k (CP n−1 ) defined by…”

“…Remark 1.2 For l = 0, Theorem 1.1 is already well-known. First, about Theorem 1.1 (i) (a), the inclusion P 0 k,n → P 0 k+1,n , which is called a stabilization map, was constructed by Guest, Kozlowski and Yamaguchi in [7,8]. Moreover, the induced homomorphism H * (P 0 k,n ; Z) → H * (P 0 k+1,n ; Z) was studied in [8].…”

“…First, about Theorem 1.1 (i) (a), the inclusion P 0 k,n → P 0 k+1,n , which is called a stabilization map, was constructed by Guest, Kozlowski and Yamaguchi in [7,8]. Moreover, the induced homomorphism H * (P 0 k,n ; Z) → H * (P 0 k+1,n ; Z) was studied in [8]. Second, about Theorem 1.1 (i) (b) and (iii) for l = 0, Guest, Kozlowski and Yamaguchi [7] and independently Kallel [9] established a more precise result.…”

Problems in Arithmetic Topology

“…Part of his proof included exhibiting homological stability via (non-algebraic) maps Rat n d (C) ֒→ Rat n d+1 (C). This work inspired many generalizations in the 40 years since, for example extending the domain to genus g ≥ 1 curves and the target to Grassmannians or toric varieties; see, for example, [12,17,43,42,51,56]. Jun-Yong Park remarked that his joint work with Changho-Han and Hunter Spink [45,72] showed stability for maps from P 1 to weighted projective spaces P(a, b).…”