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.
and Fulton, W
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2026 2verdicts
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A new extension-based construction produces strictly asymptotically Z-stable rank 3 bundles on polycyclic projective surfaces, plus a Hoppe-style criterion for rank 2 bundles.
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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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Asymptotically Z-stable bundles over projective surfaces
A new extension-based construction produces strictly asymptotically Z-stable rank 3 bundles on polycyclic projective surfaces, plus a Hoppe-style criterion for rank 2 bundles.