by J. S. Milne
Number of pages: 172
An introduction to both the geometry and the arithmetic of abelian varieties. It includes a discussion of the theorems of Honda and Tate concerning abelian varieties over finite fields and the paper of Faltings in which he proves Mordell's Conjecture.
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by Joseph M. Landsberg - arXiv
Homogeneous varieties, Topology and consequences Projective differential invariants, Varieties with degenerate Gauss images, Dual varieties, Linear systems of bounded and constant rank, Secant and tangential varieties, and more.
by Yuriy Drozd
From the table of contents: Affine Varieties; Ideals and varieties. Hilbert's Basis Theorem. Regular functions and regular mappings. Projective and Abstract Varieties; Dimension Theory; Regular and singular points; Intersection theory.
by Armand Borel, George D. Mostow - American Mathematical Society
The book covers linear algebraic groups and arithmetic groups, adeles and arithmetic properties of algebraic groups, automorphic functions and spectral decomposition of L2-spaces, vector valued cohomology and deformation of discrete subgroups, etc.
by Eckart Viehweg - Springer
This book discusses two subjects of quite different nature: Construction methods for quotients of quasi-projective schemes by group actions or by equivalence relations and properties of direct images of certain sheaves under smooth morphisms.