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 D. Gieseker - Tata Institute of Fundamental Research
These lecture notes are based on some lectures given in 1980. The object of the lectures was to construct a projective moduli space for stable curves of genus greater than or equal two using Mumford's geometric invariant theory.
by Winfried Bruns, Udo Vetter - Springer
Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. The book gives a coherent treatment of the structure of determinantal rings. The approach is via the theory of algebras with straightening law.
by Jean-Pierre Demailly - Universite de Grenoble
Basic concepts of complex geometry, coherent sheaves and complex analytic spaces, positive currents and potential theory, sheaf cohomology and spectral sequences, Hermitian vector bundles, Hodge theory, positive vector bundles, etc.
by Michael Artin - Tata Institute of Fundamental Research
These notes are based on a series of lectures given in 1973. The lectures are centered about the work of M. Scahlessinger and R. Elkik on infinitesimal deformations. Contents: Formal Theory and Computations; Elkik's Theorems on Algebraization.