Seminar

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The theory of Fano threefolds whose Picard group is generated by the anticanonical bundle (i.e., prime Fano threefolds of index one) depends crucial on the existence of certain exceptional low rank vector bundles. They yield embeddings into Grassmannians, and thereby to Mukai's biregular classifications for the deformation types of large degree. They also give rise to interesting semiorthogonal decompositions (i.e., the definition of the Kuznetsob component) in the derived category od the Fano.

I will present a proof of their existence based on the Brill-Noether theory of the K3 surfaces and curves arising as linear sections, which is joint work with Kuznetsov and Macri. To our knowledge, this is the first complete proof in the literature.