Every smooth compact submanifold of R^n is isotopically approximable by real loci of nonsingular real algebraic subsets of C^n, settling a version of Nash's conjecture with uniformity for codim >=2.
Mangolte.Real Algebraic Varieties
3 Pith papers cite this work. Polarity classification is still indexing.
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New invariants extracted from the topology of complexifications of real algebraic sets classify algebraic vector bundles over sphere products and obstruct weak algebraic approximation, disproving Kucharz-Kurdyka conjecture.
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
citing papers explorer
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Optimal embedding dimension in the Nash--Tognoli theorem
Every smooth compact submanifold of R^n is isotopically approximable by real loci of nonsingular real algebraic subsets of C^n, settling a version of Nash's conjecture with uniformity for codim >=2.
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Invariants of real affine varieties based on their complexifications
New invariants extracted from the topology of complexifications of real algebraic sets classify algebraic vector bundles over sphere products and obstruct weak algebraic approximation, disproving Kucharz-Kurdyka conjecture.
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Copositive Matrices with Ordered Off-Diagonal Entries
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.