2004/04/22 by Janós Kollár, Karen E. Smith, Alessio Corti · 118 citations
Computer Science · Mathematics · #Polynomial and algebraic computation #Rationality #Ideal (ethics) #Mathematics education #Point (geometry) #Mathematics #Algebraic number #Rational point #Algebraic variety #Computer science #Algebra over a field #Epistemology #Pure mathematics #Philosophy #Geometry
paper · doi:10.1017/cbo9780511734991
published in Cambridge University Press eBooks (Cambridge University Press)
openalex publication_date 2004/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.