Lectures on Resolution of Singularities (eBook)

János Kollár (Autor)

eBook Download: PDF

2009
Princeton University Press (Verlag)
9781400827800 (ISBN)

Infos

János Kollár is a professor of Mathematics at Princeton University.

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Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, Janos Kollar provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves, many based on the original papers of Newton, Riemann, and Noether. Kollar goes back to the original sources and presents them in a modern context. He addresses three methods for surfaces, and gives a self-contained and entirely elementary proof of a strong and functorial resolution in all dimensions. Based on a series of lectures at Princeton University and written in an informal yet lucid style, this book is aimed at readers who are interested in both the historical roots of the modern methods and in a simple and transparent proof of this important theorem.

Produkt-Details

• Erscheint lt. Verlag: 10.1.2009
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Zusatzinfo: 2 line illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• Schlagworte: Adjunction formula • algebraic closure • Algebraic Geometry • Algebraic space • algebraic surface • algebraic variety • Approximation • asymptotic analysis • automorphism • Bernhard Riemann • Big O notation • birational geometry • C0 • Canonical singularity • Codimension • cohomology • Commutative algebra • Complex Analysis • complex manifold • Computability • continuous function • coordinate system • Diagram (category theory) • differential geometry of surfaces • Dimension • Divisor • Dual graph • Du Val singularity • Embedding • Equation • equivalence relation • Euclidean algorithm • Factorization • functor • General position • Generic point • Geometric genus • Geometry • hyperplane • hypersurface • integral domain • Intersection number (graph theory) • Intersection (set theory) • Intersection theory • Irreducible component • Isolated singularity • Laurent Series • Linear space (geometry) • Linear subspace • line bundle • Mathematical Induction • Mathematics • Maximal Ideal • Morphism • Newton Polygon • Noetherian • Noetherian ring • Open problem • Open set • P-adic number • pairwise • parametric equation • partial derivative • Plane curve • polynomial • power series • Principal ideal • Principalization (algebra) • projective space • projective variety • Proper morphism • Puiseux series • Quasi-projective variety • rational function • regular local ring • Resolution of Singularities • Riemann surface • Ring Theory • Ruler • scientific notation • Sheaf (mathematics) • singularity theory • Smooth morphism • Smoothness • Special case • Subring • Summation • Surjective function • Tangent • tangent cone • Tangent Space • Taylor series • Theorem • Topology • Toric variety • Transversal (geometry) • Variable (mathematics) • Weierstrass preparation theorem • Weierstrass Theorem • Zero set
• ISBN-13: 9781400827800 / 9781400827800