A vanishing theorem of the moduli of vector bundles on curves

Jun Li
Stanford University
Mathematics

We first reconstruct the Gieseker generation of the moduli of stable vector bundles on curves. This allows us to relate the vanishing of the top Chern classes of these moduli spaces to their degenerations. By introducing a new parameter family of stabilities, we study in detail
the birational properties of these degenerations. In the end, we prove the vanishing of the top Chern classes of the moduli of rank three vector bundles on curves.


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