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(k,l)-stability

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Moduli Spaces

Narasimhan and Ramanan introduced the concept of (k,l)-stability for vector bundles over projective curves. They used the (0,1) and (1,1)-stability to compute the deformations of the moduli space M(n,d) of stable vector bundles and to define the Hecke cycles. In this lecture I will present some properties of (k,l)-stability for any k and l and describe the set A(k,l) of (k,l)-stable in terms of the Segre invariants. For certain values of k and l I will give the relation between A(k,l) and the Hilbert scheme of M(n,d).

This talk is part of the Isaac Newton Institute Seminar Series series.

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