TL;DR
This paper provides comprehensive graduate-level notes on birational geometry, emphasizing the minimal model program and related topics such as singularities, flips, and minimal models.
Contribution
It offers an in-depth, structured exposition of key concepts and techniques in birational geometry, serving as a valuable educational resource.
Findings
Detailed explanation of the minimal model program
Clarification of singularities and their role
Discussion of flips and termination processes
Abstract
This article contains the notes of a graduate course on birational geometry focusing on the minimal model program. Topics covered include singularities, vanishing, nonvanishing, cone and contraction, base point freeness, finite generation, flips, termination, minimal models and Mori fibre spaces.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry