论文标题
具有实际系数的有界多重性的非解剖系统的空间
Spaces of non-resultant systems of bounded multiplicity with real coefficients
论文作者
论文摘要
对于每对$（m，n）$的正整数，带有$（m，n）\ not =（1,1）$和一个任意字段$ \ bf f $，带有代数关闭$ \ overline {\ bf f} $，让$ \ rm po^rm po^{d，m} _n（d，m} _n（\ bf f） $（f_1（z），\ cdots，f_m（z））\ in \ bf f [z]^m $ of $ \ bf f $ - 相同程度$ d $的一元多项式，使得polynomials $ \ \ \ \ \ \ \ {f_k（z）\}多重性$ \ geq n $。这些空间$ \ rm po^{d，m} _n（\ bf f）$首先由B. Farb和J. Wolfson定义和研究为Arnold，Vassiliev和Segal和其他其他不同背景下首先研究的空间的概括。在以前，我们在情况下明确确定了此空间的同置类型$ \ bf f = \ bbb c $。在本文中，我们调查了$ \ bf f = \ bbb r $的情况。
For each pair $(m,n)$ of positive integers with $(m,n)\not= (1,1)$ and an arbitrary field $\bf F$ with algebraic closure $\overline{\bf F}$, let $\rm Po^{d,m}_n(\bf F)$ denote the space of $m$-tuples $(f_1(z),\cdots ,f_m(z))\in \bf F [z]^m$ of $\bf F$-coefficients monic polynomials of the same degree $d$ such that the polynomials $\{f_k(z)\}_{k=1}^m$ have no common root in $\overline{\bf F}$ of multiplicity $\geq n$. These spaces $\rm Po^{d,m}_n(\bf F)$ were first defined and studied by B. Farb and J. Wolfson as generalizations of spaces first studied by Arnold, Vassiliev and Segal and others in several different contexts. In previous we determined explicitly the homotopy type of this space in the case $\bf F =\Bbb C$. In this paper, we investigate the case $\bf F =\Bbb R$.
