ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14 Avritzer, Dan, Universidade Federal de Minas Gerais, Brasil: The Hilbert scheme component of the intersection of two quadrics A description of the irreducible component of the Hilbert scheme parametrizing complete intersections of two quadrics in P^{n} for n ≥ 3 will be presented. The main result is that this component is isomorphic to a double blowup of the Grassmannian of pencils of quadrics in P^{n}. This is a generalization of [1]. Applications to enumerative geometry will be given. Some of the numbers found were later obtained by E. Getzler [2] using other methods. These results are joint work with I. Vainsencher. References:1. D. Avritzer and I. Vainsencher, Compactifying the Space of Elliptic Quartic Curves, Complex Projective Geometry, G. Ellingsrud, C. Peskine, G. Sacchiero and S. Strømme eds., London Math. Soc. LNS, 179, C. U. P. (1992).

2. E. Getzler, Intersection Theory on \overline{M}_{1,4} and Elliptic-Gromov Invariants, to appear.