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The Period Lattice for Enriques Surfaces Daniel Allcock*

The Period Lattice for Enriques Surfaces

Daniel Allcock*
14 May 1999
MSC: 14J28 (11F55, 11E12)

It is well-known that the isomorphism classes of complex Enriques surfaces ar*
*e in 1-1 correspon-
dence with a Zariski-open subset (D - H)= of the quotient of the Hermitian s*
*ymmetric space D
for O(2, 10). Here H is a totally geodesic divisor in D and is a certain ar*
*ithmetic group. In the
usual formulation of this result [5], is described as the isometry group of*
* a certain integral lattice
N of signature (2, 10). This lattice is quite complicated, and requires sophi*
*sticated techniques to
work with. The purpose of this note is to replace N by the much simpler latti*


Source: Allcock, Daniel - Department of Mathematics, University of Texas at Austin


Collections: Mathematics