A characterization of the complex affine line.
The Runge approximation problem for holomorphic maps into Grassmannians.
On homology of real algebraic sets.
Rational functions without poles in a compact set
Let X be an irreducible nonsingular complex algebraic set and let K be a compact subset of X. We study algebraic properties of the ring of rational functions on X without poles in K. We give simple necessary conditions for this ring to be a regular ring or a unique factorization domain.
Nash cohomology of smooth manifolds
A Nash cohomology class on a compact Nash manifold is a mod 2 cohomology class whose Poincaré dual homology class can be represented by a Nash subset. We find a canonical way to define Nash cohomology classes on an arbitrary compact smooth manifold M. Then the Nash cohomology ring of M is compared to the ring of algebraic cohomology classes on algebraic models of M. This is related to three conjectures concerning algebraic cohomology classes.
Realization of homotopy classes by algebraic mappings.
On relative real holomorphy rings.
Algebraic, Rational, and homological equivalence of real cycles.
Nonisomorphic algebraic models of a smooth manifold.
Real algebraic hypersurfaces in complex projective varieties.
On polynomial mappings into spheres
Approximation of holomorphic maps by algebraic morphisms
Let X be a nonsingular complex algebraic curve and let Y be a nonsingular rational complex algebraic surface. Given a compact subset K of X, every holomorphic map from a neighborhood of K in X into Y can be approximated by rational maps from X into Y having no poles in K. If Y is a nonsingular projective complex surface with the first Betti number nonzero, then such an approximation is impossible.
Morphisms, line bundles and moduli spaces in real algebraic geometry
Almost Analytic Local Algebraicity of Analytic Sets and Functions.
On Equivalence of Ideals of Real Global Analytic Functions and the 17th Hilbert Problem.
On Algebraicity of Global Real Analytic Sets and Functions
Equivalence of analytic and rational functions
We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.
Polynomial mappings form products of algebraic sets into spheres.
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