Algorithms in Real Algebraic Geometry
by S. Basu, R. Pollack, M. Roy
Publisher: Springer 2009
Number of pages: 672
The monograph gives a self-contained detailed exposition of the algorithmic real algebraic geometry. In general, the monograph is well written and will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields.
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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 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 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.
by Michel Coste - Universite de Rennes
Semialgebraic geometry is the study of sets of real solutions of systems of polynomial equations and inequalities. These notes present the first results of semialgebraic geometry and related algorithmic issues. Their content is by no means original.