The homotopy type of spaces of real resultants with bounded multiplicity

DOI10.2969/JMSJ/79897989zbMATH Open1506.55007arXiv1803.02154OpenAlexW2793280661MaRDI QIDQ2093637

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Publication date: 27 October 2022

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Abstract: For positive integers

d, m, n g e q 1

with

(m, n) o t = (1, 1)

and

B b b K = B b b R

or

B b b C

, let

Q_{n}^{d, m} (B b b K)

denote the space of

m

-tuples

(f_{1} (z), c d o t s, f_{m} (z)) i n B b b K [z]^{m}

of

B b b K

-coefficients monic polynomials of the same degree

d

such that polynomials

{f_{k} (z)}_{k = 1}^{m}

have no common {it real} root of multiplicity

g e q n

(but may have complex common root of any multiplicity). %% These spaces can be regarded as one of generalizations of the spaces defined and studied by Arnold and Vassiliev, and they may be also considered as the real analogues of the spaces studied by B. Farb and J. Wolfson. In this paper, we shall determine their homotopy types explicitly and generalize some previously obtained results.

Full work available at URL: https://arxiv.org/abs/1803.02154

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