Morphisms, line bundles and moduli spaces in real algebraic geometry

Bochnak, Jacek; Kucharz, Wojciech; Silhol, Robert

doi:10.1007/bf02698917

Cited by 12 publications

(8 citation statements)

References 22 publications

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“…In particular real rational models of surfaces were studied in [2,22] and approximations of smooth maps to spheres by real algebraic morphisms were investigated in [3][4][5]11,12,18,22].…”

Section: (History Of Related Questions)mentioning

confidence: 99%

Cremona transformations and diffeomorphisms of surfaces

Kollár¹,

Mangolte²

2009

Advances in Mathematics

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“…In particular real rational models of surfaces were studied in [2,22] and approximations of smooth maps to spheres by real algebraic morphisms were investigated in [3][4][5]11,12,18,22].…”

Section: (History Of Related Questions)mentioning

confidence: 99%

Cremona transformations and diffeomorphisms of surfaces

Kollár¹,

Mangolte²

2009

Advances in Mathematics

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“…We say that a topological F-vector bundle on X (R) admits an algebraic structure if it is isomorphic to E(F)| X (R) for some U and E as above. This terminology is consistent with that used in [6,10,11,13], X (R) being Zariski dense in X . In this section, we are interested in the subgroup…”

Section: Algebraic Models and Vector Bundlesmentioning

confidence: 60%

Complex cycles on algebraic models of smooth manifolds

Kucharz

2009

Math. Ann.

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Every compact smooth manifold M is diffeomorphic to the set X (R) of real points of a nonsingular projective real algebraic variety X , which is called an algebraic model of M. Each algebraic cycle of codimension k on the complex variety X C = X × R C determines a cohomology class in H 2k (X (R); D), where D denotes Z or Q. We investigate the behavior of such cohomology classes as X runs through the class of algebraic models of M.

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“…In other words, the problem is to find a characterization of these maps in C(X, Y ) that can be approximated by either regular or X -regular or stratified-regular maps. Approximation by regular maps is investigated in [9,10,12,13,16,18]. As demonstrated in [33,35], stratified-regular maps are much more flexible than regular maps.…”

Section: Approximation By Stratified-regular Mapsmentioning

confidence: 99%

“…Algebraic and C-algebraic cohomology classes have many applications in real algebraic geometry, cf. [1,2,5,6,8,9,10,12,13,14,16,17,18,19,33,35]. We introduce stratified-algebraic and stratified-C-algebraic cohomology classes in Section 7 and Section 8, respectively.…”

mentioning

confidence: 99%

Stratified-algebraic vector bundles

Kucharz

Kurdyka

2016

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Abstract We investigate stratified-algebraic vector bundles on a real algebraic variety X. A stratification of X is a finite collection of pairwise disjoint, Zariski locally closed subvarieties whose union is X. A topological vector bundle ξ on X is called a stratified-algebraic vector bundle if, roughly speaking, there exists a stratification {\mathcal{S}} of X such that the restriction of ξ to each stratum S in {\mathcal{S}} is an algebraic vector bundle on S. In particular, every algebraic vector bundle on X is stratified-algebraic. It turns out that stratified-algebraic vector bundles have many surprising properties, which distinguish them from algebraic and topological vector bundles.

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Morphisms, line bundles and moduli spaces in real algebraic geometry

Cited by 12 publications

References 22 publications

Cremona transformations and diffeomorphisms of surfaces

Cremona transformations and diffeomorphisms of surfaces

Complex cycles on algebraic models of smooth manifolds

Stratified-algebraic vector bundles

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