Rational homology of spaces of complex monic polynomials with multiple roots

Details Rational homology of spaces of complex monic polynomials with multiple roots Rational homology of spaces of complex monic polynomials with multiple roots

2001-11-14

arxiv.org/abs/math/0111167v1

Mathematika 49 (2002), no. 1-2, 77--91 (2004).

Mathematics

Combinatorics

Scientific paper

We study rational homology groups of one-point compactifications of spaces of complex monic polynomials with multiple roots. These spaces are indexed by number partitions. A standard reformulation in terms of quotients of orbit arrangements reduces the problem to studying certain triangulated spaces $X_{\lambda,\mu}$. We present a combinatorial description of the cell structure of $X_{\lambda,\mu}$ using the language of marked forests. As applications we obtain a new proof of a theorem of Arnold and a counterexample to a conjecture of Sundaram and Welker, along with a few other smaller results.

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