ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14, 55, 32 Bhosle, Usha N., Tata Institute of Fundamental Research, India Moduli spaces of torsion-free sheaves on nodal curves We study moduli spaces U_{Y} (n, d) (resp. U_{Y} (n, L)) of semistable torsionfree sheaves of rank n, degree d (resp. with a “fixed determinant L”) on a reduced connected nodal curve Y. Explicit descriptions of U_{Y} (2, L) are obtained in case Y is hyperelliptic. The relation between representations of π_{1}(Y) in GL(n, C) and vector bundles on Y is studied. Examples of stable bundles which do not come from representations and whose tensor products etc. are not semistable are constructed. Normalisations of U_{Y} (n, d), U_{Y} (n, L) are obtained using parabolic bundles. It is shown that if Y is irreducible and U′_{Y} (n, L) (resp. U_{Y}^{′s}(n, L)) denote the subsets corresponding to vector bundles (resp. stable vector bundles) then Pic U′_{Y} (n, L) ≈ Z/(m), Pic U_{Y}^{′s}(n, L) ≈ Z for almost all n, d . Results are extended to principal G bundles on Y. References. Bhosle Usha N. : Representations of the fundamental group and vector bundles. Math. Ann. 302,601–608 (1995). Vector bundles on curves with many components. To appear in Proc. London Math. Soc.