The homotopy type of spaces of resultants of bounded multiplicity
The homotopy type of spaces of resultants of bounded multiplicity
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有界重数合力空间的同伦型
DOI：
10.1016/j.topol.2017.10.002
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Kozlowski and K. Yamaguchi
中科院分区：
文献类型：
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作者：
Kozlowski A.;Yamaguchi K.;K. Yamaguchi;Masahiro Ohno;A. Kozlowski and K. Yamaguchi
对于具有(m，n)≥(1，1)的整数m，n，d≠1和具有代数闭包F‾的域F，设Poly d，m n(F)表示所有m元组(f1(Z)，…，f m(Z))∈F[z]m，使得多项式f 1(Z)，…这些空间是由Farb和Wolfson[12]定义的，它们是Arnold，Vassiliev，‾等人在不同背景下首先研究的空间的推广。他们得到了关于它们的代数、几何和算术结果。在本文中，我们研究了F=C情形下这些空间的同伦型。我们的结果推广了文献[12]关于F=C的结果，也推广了G.西格尔[28]、V.Vassiliev[30]和F.Cohen-R.Cohen-B.Mann-R.Milgram[5]关于m≥2和n≥2的结果。
For integers m, n, d≥ 1 with (m, n)≠(1, 1) and a field F with algebraic closure F‾, let Poly d, m n (F) denote the space of all m-tuples (f 1 (z),…, f m (z))∈ F [z] m of monic polynomials of the same degree d such that polynomials f 1 (z),…, f m (z) have no common root in F‾ of multiplicity≥ n. These spaces were defined by Farb and Wolfson [12] as generalizations of spaces first studied by Arnold, Vassiliev, Segal and others in different contexts. They obtained algebraic geometrical and arithmetic results about them. In this paper we investigate the homotopy type of these spaces for the case F= C. Our results generalize those of [12] for F= C and also results of G. Segal [28], V. Vassiliev [30] and F. Cohen–R. Cohen–B. Mann–R. Milgram [5] for m≥ 2 and n≥ 2.