The Geometry of some special Arithmetic Quotients

The book discusses a series of higher-dimensional moduli spaces, of abelian varieties, cubic and K3 surfaces, which have embeddings in projective spaces as very special algebraic varieties. Many of these were known classically, but in the last chapter a new such variety, a quintic fourfold, is introduced and studied. The text will be of interest to all involved in the study of moduli spaces with symmetries, and contains in addition a wealth of material which has been only accessible in very old sources, including a detailed presentation of the solution of the equation of 27th degree for the lines on a cubic surface.

Contenu

Moduli spaces of PEL structures.- Arithmetic quotients.- Projective embeddings of modular varieties.- The 27 lines on a cubic surface.- The Burkhardt quartic.- A gem of the modular universe.