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Restrictions of stable bundles. (English) Zbl 1386.14157

Alexeev, Valery (ed.) et al., Compact moduli spaces and vector bundles. Conference on compact moduli and vector bundles, University of Georgia, Athens, GA, USA, October 21–24, 2010. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-6899-7/pbk). Contemporary Mathematics 564, 177-184 (2012).
Summary: The Mehta-Ramanathan theorem ensures that the restriction of a stable vector bundle to a sufficiently high degree complete intersection curve is again stable. We improve the bounds for the ”sufficiently high degree” and propose a possibly optimal conjecture.
For the entire collection see [Zbl 1236.14001].

MSC:

14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14C05 Parametrization (Chow and Hilbert schemes)
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
32L05 Holomorphic bundles and generalizations
32Q26 Notions of stability for complex manifolds
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