The geometry of the moduli spaces has also been studied, though perhaps less thoroughly than the topology. This lecture will describe some of these geometrical aspects, especially the Segre stratification and Brill-Noether theory.

References

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• U. N. Bhosle, Moduli of orthogonal and spin bundles on hyperelliptic curves, Comp. Math. 51 (1984), 15-40.
• M. Teixidor i Bigas, Brill-Noether theory for stable vector bundles, Duke Math. J. 62 (1991), 385-400.
• L. Brambila-Paz, I. Grzegorczyk and P. E. Newstead, Geography of Brill-Noether loci for small slopes, J. Alg. Geom. 6 (1997), 645-669.
• V. Mercat, Le probleme de Brill-Noether pour les fibres stables de petite pente, J. Reine Angew. Math. 506 (1999), 1-14.
• L. Brambila-Paz, V. Mercat. P. E. Newstead and F. Ongay, Nonemptiness of Brill-Noether loci, Internat. J. Math. 11 (2000), 737-760.
• H. Lange and M. S. Narasimhan, Maximal subbundles of rank 2 vector bundles on curves, Math. Ann. 266 (1983), 55-72.
• L. Brambila-Paz and H. Lange, A stratification of the moduli space of vector bundles on curves, J. Reine Angew. Math. 499 (1998), 173-187.
• B. Russo and M. Teixidor i Bigas, On a conjecture of Lange, J. Alg. Geom. 8 (1999), 483-496.