Vector bundles on a \(K3\) surface. (English) Zbl 1046.14016
Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20–28, 2002. Vol. II: Invited lectures. Beijing: Higher Education Press; Singapore: World Scientific/distributor (ISBN 7-04-008690-5/3-vol. set). 495-502 (2002).
Summary: A \(K3\) surface is a quaternionic analogue of an elliptic curve from a view point of moduli of vector bundles. We can prove the algebraicity of certain Hodge cycles and rigidity of a curve of genus eleven. We give two kinds of descriptions of Fano threefolds as applications. In the final section we discuss a simplified construction of moduli spaces.
For the entire collection see [Zbl 0993.00022].
For the entire collection see [Zbl 0993.00022].
MSC:
| 14J28 | \(K3\) surfaces and Enriques surfaces |
| 14J60 | Vector bundles on surfaces and higher-dimensional varieties, and their moduli |
| 14H51 | Special divisors on curves (gonality, Brill-Noether theory) |
| 14C30 | Transcendental methods, Hodge theory (algebro-geometric aspects) |
| 14C05 | Parametrization (Chow and Hilbert schemes) |
