Lectures on Logarithmic Algebraic Geometry
by Arthur Ogus
Publisher: University of California, Berkeley 2006
Number of pages: 255
Logarithmic geometry was developed to deal with two fundamental and related problems in algebraic geometry: compactification and degeneration. Contents: The geometry of monoids; Log structures and charts; Morphisms of log schemes; Differentials and smoothness; De Rham and Betti cohomology.
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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 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 Johan de Jong, et al.
The stacks project aims to build up enough basic algebraic geometry as foundations for algebraic stacks. This implies a good deal of theory on commutative algebra, schemes, varieties, algebraic spaces, has to be developed en route.
by D. Eisenbud, D. Grayson, M. Stillman, B. Sturmfels - Springer
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.