Computations in Algebraic Geometry with Macaulay 2
by D. Eisenbud, D. Grayson, M. Stillman, B. Sturmfels
Publisher: Springer 2001
Number of pages: 343
This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications.
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by P. Samuel - Tata Institute Of Fundamental Research
The aim of this text is to give a proof, due to Hans Grauert, of an analogue of Mordell's conjecture. Contents: Introduction; Algebro-Geometric Background; Algebraic Curves; The Theorem of Grauert (Mordell's conjecture for function fields).
by Masayoshi Miyanishi - Tata Institute of Fundamental Research
From the table of contents: Introduction; Geometry of the affine line (Locally nilpotent derivations, Algebraic pencils of affine lines, Flat fibrations by the affine line); Curves on an affine rational surface; Unirational surfaces; etc.
by Enrique Arrondo - Universidad Complutense de Madrid
The scope of these notes is to present a soft and practical introduction to algebraic geometry, i.e. with very few algebraic requirements but arriving soon to deep results and concrete examples that can be obtained 'by hand'.
by Donu Arapura - Purdue University
Algebraic geometry is the geometric study of sets of solutions to polynomial equations over a field (or ring). In this book the author maintains a reasonable balance between rigor and intuition; so it retains the informal quality of lecture notes.