11 citations · 47 across the 48 of their papers we have counts for
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Sharp bounds on fake weighted projective spaces with canonical singularities
Gennadiy Averkov, Alexander Kasprzyk, Martin Lehmann +1
We give a sharp upper bound on the multiplicity of a fake weighted projective space with at worst canonical singularities. This is equivalent to giving a sharp upper bound on the i…
Constructive proofs of some positivstellensätze for compact semialgebraic subsets of
Gennadiy Averkov
In a broad sense, positivstellensätze are results about representations of polynomials which are strictly positive on a given set. We give constructive and, to a large extent, elem…
Minimal polynomial descriptions of polyhedra and special semialgebraic sets
Gennadiy Averkov, Ludwig Bröcker
We show that a -dimensional polyhedron in can be represented by -polynomial inequalities, that is, $S = \{x \in \real^d : p_0(x) \ge 0, >..., p_{d-1}(x) \ge 0 \…
Notes on algebra and geometry of polynomial representations
Gennadiy Averkov
Consider a semi-algebraic set A in R^d constructed from the sets which are determined by inequalities p_i(x)>0, p_i(x)\ge 0, or p_i(x)=0 for a given list of polynomials p_1,...,p_m…
Representing elementary semi-algebraic sets by a few polynomial inequalities: A constructive approach
Gennadiy Averkov
Let P be an elementary closed semi-algebraic set in R^d, i.e., there exist real polynomials p_1,...,p_s such that P= \{x \in R^d : p_1(x) \ge 0, >..., p_s(x) \ge 0 \}; in this case…