Clay Mathematics Proceedings | The Resolution of Singular Algebraic Varieties

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1. Lecture I: A First Example of Resolution 

2. Lecture II: Varieties and Schemes 

3. Lecture III: Singularities 

4. Lecture IV: Blowups 

5. Lecture V: Properties of Blowup 

6. Lecture VI: Transforms of Ideals and Varieties under Blowup 

7. Lecture VII: Resolution Statements 

8. Lecture VIII: Invariants of Singularities 

9. Lecture IX: Hypersurfaces of Maximal Contact 

10. Lecture X: Coefficient Ideals 

11. Lecture XI: Resolution in Zero Characteristic 

12. Lecture XII: Positive Characteristic Phenomena 

13. Discussion of selected examples