Séminaire Lotharingien de Combinatoire, B34h (1995), 15pp.
Jürgen Richter-Gebert
Mnëv's Universality Theorem Revisited
Abstract.
This article presents a complete proof of Mnëv's Universality
Theorem and a complete proof of Mnëv's Universal Partition Theorem
for oriented matroids. The Universality Theorem states that, for every
primary semialgebraic set V there is an oriented matroid M, whose
realization space is stably equivalent to V. The Universal
Partition Theorem states that, for every partition V of
Rn indiced by m polynomial functions
f(1),...,f(n) with integer coefficients there is a corresponding family
of oriented matroids (M(s)), with s ranging in the set of m-tuples
with elements in {-1,0,+1}, such that the collection of their realization
spaces is stably equivalent to the family V.
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