ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14 Brînzǎnescu, Vasile, Institute of Mathematics, Bucharest, Romania Moduli spaces of stable 2-vector bundles over ruled surfaces Let π : X → C be a ruled surface. We define two numerical invariants d and r for an algebraic 2-vector bundle with fixed Chern classes c_{1} and c_{2} and let M(c_{1}, c_{2}, d, r) be the set of isomorphism classes of bundles with fixed invariants c_{1}, c_{2}, d, r. We give necessary and sufficient conditions for the non-emptiness of M(c_{1}, c_{2}, d, r). Then, we get effective bounds of the Chern class c_{2} for the non-emptiness of moduli spaces of stable 2-vector bundles over X. Part of these results is joint work with M. Aprodu. References: M. Aprodu, and V. Brînzǎnescu, C. R. Acad. Sci. Paris 323 (1996), 627–630; C. R. Acad. Sci. Paris 325 (1997), 295–300.