Vector bundles on smooth affine threefolds
Speaker: Dr. Jean Fasel (Universitaet Duisburg-Essen)
Time: 4.00 PM
Date: Monday 21st October 2013
Location: Casl Seminar Room Block 8 (Belfield Office Park)
Abstract:
Given a smooth affine variety X of Krull dimension d over a field k and an integer r, the problem to understand the set VB_r(X) of isomorphism classes of vector bundles of rank r over X has been extensively studied. If r>d, then a classical result of Serre asserts that VB_r(X) is in bijection with the reduced K_0 of X and can thus be computed using the full machinery of K-theory. If r is less or equal to d, then such a result is in general wrong. However, some things can still be said. For instance, the cases when X is a curve or a surface have been completely understood for quite a while. In this talk we will give a survey of recent results when X is a threefold.
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