Introduction to Singularities

Shihoko Ishii is a professor emeritus at the University of Tokyo and a professor at the Tokyo Woman's Christian University.

• 1. Sheaves, algebraic varieties and analytic spaces.- 2. Homological algebra and duality.- 3. Singularities, algebraization and resolutions of singularities.- 4. Divisors on a variety and the corresponding sheaves.- 5. Differential forms around the singularities.- 6. Two dimensional singularities.- 7. Higher dimensional singularities.- 8. Deformations of singularities.