%0 Journal Article %T Vector bundles on a K3 surface %A Shigeru Mukai %J Mathematics %D 2003 %I arXiv %X 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 a rigidity of curve of genus eleven and gives two kind of descriptions of Fano threefolds as applications. In the final section we discuss a simplified construction of moduli spaces. %U http://arxiv.org/abs/math/0304303v1