ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14, 51, 20 Nieto, B. Isidro, Instituto de Fisica y Matematicas de la Universidad Michoacana de SNH, MEXICO : Poster Presentation: H_{2,2}-Kummer surfaces associated to polarized abelian surfaces of type (1,3). Let H_{2,2} be the Heisenberg group of level 2. In [BN] a threefold M ⊂ Gr(1, 3) and a quintic hypersurface N ⊂ P_{4} have been introduced. By passing to the quotient with H_{2,2} a map ν : M/H_{2,2} → N which is only defined on an open part of N, N^{s}. Similarly, one defines an open part M^{s} of M. We define ν for N^{s} so that to each point of M^{s}/H_{2,2} there corresponds a H_{2,2}-Kummer surface containing a line corresponding to this point. We describe explicitely the ramification locus of ν as a codimension one subvariety of N. Using [§6 of BN] M^{s}/H_{2,2} is identified with an open part of A_{(1,3)}(2) , the moduli space of polarized abelian surfaces with a level 2-structure. We describe explicitely the subvarieties of the above moduli space with the subvarieties of the ramification locus of ν as has been recently described in a recent joint paper [HNS]. References [BN] Barth, W. Nieto, I. Abelian surfaces of type (1,3) and quartic surfaces with 16 skew lines, Journ. alg. geom. 1994, 173-222.

[HNS] Hulek, K., Nieto, I., Sankaran, G. Heisenberg Invariant Kummer Surfaces I, preprint U. of Bath, 1998.