Let RX l k,n be the space consisting of all (n + 1)–tuples (p 0 (z),. .. , p n (z)) of monic polynomials over R of degree k and such that there are at most l roots common to all p i (z). In this paper, we prove a stable splitting of RX l k,n .
The homology of spaces of polynomials with roots of bounded multiplicity YASUHIKO KAMIYAMA Let P l k,n be the space consisting of monic complex polynomials f (z) of degree k and such that the number of n–fold roots of f (z) is at most l. In this paper, we determine the integral homology groups of P l k,n .
For an algebraically closed field K with ch(K) = 2, let OM (1, SO(n, K)) denote the moduli space of holomorphic bundles on P 2 with the structure group SO(n, K) and half the first Pon-tryagin index being equal to 1, each of which is trivial on a fixed line l ∞ and has a fixed holomorphic trivialization there. In this paper we determine the Chow ring of OM… (More)
The purpose of this article is to (1) define M (t, k) the t-fold center of mass arrangement for k points in the plane, (2) give elementary properties of M (t, k) and (3) give consequences concerning the space M (2, k) of k distinct points in the plane, no four of which are the vertices of a parallelogram. The main result proven in this article is that the… (More)