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. §0. Notation and Conventions. Chapter 1. Filtered Rings and Filtered Blowing-Ups. § 1. Filtered Blowing-Up and the Induced Filtration on Local Cohomology Groups. § 2. The Divisor Class Group of Normal Rees Algebras. § 3. The Dualizing Module on the Filtered Blowing-Up and the Criterion for Gorenstein Property. Appendix to § 3. Graded Dualizing Complex for Graded Rings and Duality for Projective Morphisms. § 4. Criterion for Normality and Rational Singularity § 5. The Case When G Has an Isolated Singularity. Chapter 2. Normal Two-Dimensional Singularities with "Star-Shaped" Resolution. § 6. "Star-Shaped" Resolution and the Filtration. § 7. Gorenstein Singularities with "Star-Shaped" Resolution. § 8. The Case with pa = 2. References.

Filtered rings, filtered blowing-ups and normal two-dimensional singularities with ``star-shaped'' resolution