Lectures on Resolution of Singularities (AM-166) / / János Kollár.
Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, János Kollár 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. K...
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2009] ©2007 |
| Year of Publication: | 2009 |
| Edition: | Course Book |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
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Kollár, János, author. aut http://id.loc.gov/vocabulary/relators/aut Lectures on Resolution of Singularities (AM-166) / János Kollár. Course Book Princeton, NJ : Princeton University Press, [2009] ©2007 1 online resource (208 p.) : 2 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 166 Frontmatter -- Contents -- Introduction -- Chapter 1. Resolution for Curves -- Chapter 2. Resolution for Surfaces -- Chapter 3. Strong Resolution in Characteristic Zero -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, János Kollár 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. Kollár 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Mathematics Geometry Algebraic. Singularities (Mathematics). MATHEMATICS / Geometry / Algebraic. bisacsh 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. Du Val singularity. Dual graph. Embedding. Equation. Equivalence relation. Euclidean algorithm. Factorization. Functor. General position. Generic point. Geometric genus. Geometry. Hyperplane. Hypersurface. Integral domain. Intersection (set theory). Intersection number (graph theory). Intersection theory. Irreducible component. Isolated singularity. Laurent series. Line bundle. Linear space (geometry). Linear subspace. Mathematical induction. Mathematics. Maximal ideal. Morphism. Newton polygon. Noetherian ring. Noetherian. 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 cone. Tangent space. Tangent. Taylor series. Theorem. Topology. Toric variety. Transversal (geometry). Variable (mathematics). Weierstrass preparation theorem. Weierstrass theorem. Zero set. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691129235 https://doi.org/10.1515/9781400827800?locatt=mode:legacy https://www.degruyter.com/isbn/9781400827800 Cover https://www.degruyter.com/document/cover/isbn/9781400827800/original |
| language |
English |
| format |
eBook |
| author |
Kollár, János, Kollár, János, |
| spellingShingle |
Kollár, János, Kollár, János, Lectures on Resolution of Singularities (AM-166) / Annals of Mathematics Studies ; Frontmatter -- Contents -- Introduction -- Chapter 1. Resolution for Curves -- Chapter 2. Resolution for Surfaces -- Chapter 3. Strong Resolution in Characteristic Zero -- Bibliography -- Index |
| author_facet |
Kollár, János, Kollár, János, |
| author_variant |
j k jk j k jk |
| author_role |
VerfasserIn VerfasserIn |
| author_sort |
Kollár, János, |
| title |
Lectures on Resolution of Singularities (AM-166) / |
| title_full |
Lectures on Resolution of Singularities (AM-166) / János Kollár. |
| title_fullStr |
Lectures on Resolution of Singularities (AM-166) / János Kollár. |
| title_full_unstemmed |
Lectures on Resolution of Singularities (AM-166) / János Kollár. |
| title_auth |
Lectures on Resolution of Singularities (AM-166) / |
| title_alt |
Frontmatter -- Contents -- Introduction -- Chapter 1. Resolution for Curves -- Chapter 2. Resolution for Surfaces -- Chapter 3. Strong Resolution in Characteristic Zero -- Bibliography -- Index |
| title_new |
Lectures on Resolution of Singularities (AM-166) / |
| title_sort |
lectures on resolution of singularities (am-166) / |
| series |
Annals of Mathematics Studies ; |
| series2 |
Annals of Mathematics Studies ; |
| publisher |
Princeton University Press, |
| publishDate |
2009 |
| physical |
1 online resource (208 p.) : 2 line illus. Issued also in print. |
| edition |
Course Book |
| contents |
Frontmatter -- Contents -- Introduction -- Chapter 1. Resolution for Curves -- Chapter 2. Resolution for Surfaces -- Chapter 3. Strong Resolution in Characteristic Zero -- Bibliography -- Index |
| isbn |
9781400827800 9783110494914 9783110442502 9780691129235 |
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Q - Science |
| callnumber-subject |
QA - Mathematics |
| callnumber-label |
QA614 |
| callnumber-sort |
QA 3614.58 |
| genre_facet |
Geometry Algebraic. |
| url |
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| illustrated |
Illustrated |
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500 - Science |
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510 - Mathematics |
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516 - Geometry |
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516.3/5 |
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3516.3 15 |
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516.3/5 |
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516.3/5 |
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