Introduction to Singularities Book by Shihoko Ishii
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Introduction to Singularities

Introduction to Singularities


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About the Book

​0. Preliminaries: Variations of making singularities0.1. By cutting-hypersurface singularities, hyperplane section of singularities0.2. By taking quotients-quotient singularities, quotient of singularities0.3. By lifting up-covering singularities0.4. By contractions 1. Sheaves, algebraic varieties and analytic spaces1.1. Preliminaries on sheaves1.2. Sheaves on a topological space1.3. Analytic space and Algebraic variety1.4. Coherent sheaves2. Homological algebra and duality2.1. Injective resolutions2.2. i-th derived functors2.3. Ext2.4. Cohomologies with the coefficients on sheaves2.5. Derived functors and duality2.6. Spectral sequence3. Singularities, algebraization and resolutions of singularities3.1. Definition of a singularity3.2. Algebraization theorem3.3. Blowups and resolutions of the singularities3.4. Toric resolutions of the singularities4. Divisors on a variety and the corresponding sheaves4.1. Locally free sheaves, invertible sheaves and divisorial sheaves4.2. Divisors4.3. The canonical sheaves and a canonical divisor4.4. Intersections of divisors5. Differential forms around the singularities5.1. Ramification formula5.2. Canonical singularities, terminal singularities and rational singularities6. Two dimensional singularities6.1. Resolutions of two-dimensional singularities6.2. The fundamental cycle6.3. Rational singularities6.4. Quitient singularities6.5. Rational double points6.6. Elliptic singularities6.7. Two-dimensional Du Bois singularities6.8. Classification of two-dimensional singularities by κ7. Higher dimensional singularities7.1. Mixed Hodge structures and Du Bois singularities7.2. Minimal model problem7.3. Higher dimensional canonical singularities and terminal singularities7.4. Higher dimensional 1-Gorenstein singularities8. Deformations of singularities8.1. Change of properties under deformations8.2. Versal deformationsAppendix: Recent resultsReferences


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Product Details
  • ISBN-13: 9784431562610
  • Publisher: Springer Verlag, Japan
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 223
  • Series Title: English
  • Weight: 381 gr
  • ISBN-10: 4431562613
  • Publisher Date: 23 Aug 2016
  • Edition: Softcover reprint of the original 1st ed. 2014
  • Language: English
  • Returnable: Y
  • Spine Width: 12 mm
  • Width: 156 mm


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Introduction to Singularities
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Introduction to Singularities
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