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Vector bundles on real algebraic curves

100%
Maciejewski Ł.
Universitatis Iagellonicae Acta Mathematica
|
2012
|
vol. 50
63-68
EN
We prove that any topological real line bundle on a compact real algebraic curve $X$ is isomorphic to an algebraic line bundle. The result is then generalized to vector bundles of an arbitrary constant rank. As a consequence we prove that any continuous map from $X$ into a real Grassmannian can be approximated by regular maps.
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