Vector bundles over real algebraic surfaces and threefolds
Real Algebraic Curves as Complete Intersections.
Sums of 2 n-th Powers of Real Meromorphic Functions.
Invertible ideals in real holomorphy rings.
On analytic sets and functions with given isolated singularities.
Algebraic cycles and vector bundles on real affine threefolds.
Homology classes of real algebraic sets
There is a large research program focused on comparison between algebraic and topological categories, whose origins go back to 1952 and the celebrated work of J. Nash on real algebraic manifolds. The present paper is a contribution to this program. It investigates the homology and cohomology classes represented by real algebraic sets. In particular, such classes are studied on algebraic models of smooth manifolds.
Splitting vector bundles by blowups
We show some advantages of splitting vector bundles by blowups.
Cycles on algebraic models of smooth manifolds
Every compact smooth manifold is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of . We study modulo 2 homology classes represented by algebraic subsets of , as runs through the class of all algebraic models of . Our main result concerns the case where is a spin manifold.
Approximation by continuous rational maps into spheres
Investigated are continuous rational maps of nonsingular real algebraic varieties into spheres. In some cases, necessary and sufficient conditions are given for a continuous map to be approximable by continuous rational maps. In particular, each continuous map between unit spheres can be approximated by continuous rational maps.
Local algebraicity of analytic sets.
Algebraic models of smooth manifolds.
On homology classes represented by real algebraic varieties
Algebraic equivalence of real algebraic cycles
Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.
On approximation of smooth submanifolds by nonsingular real algebraic subvarieties
Erratum to : Morphisms, line bundles and moduli spaces in real algebraic geometry
Codimension two transcendental submanifolds of projective space
We provide a simple characterization of codimension two submanifolds of that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when . If the codimension two submanifold is a nonsingular algebraic subset of whose Zariski closure in is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in .
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