Extremal Singularities

Extremal Singularities

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Example: Cubic cones of dimension two

7 of 14

7 of 14

Example: Cubic cones of dimension two

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Classroom Contents

Extremal Singularities

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  1. 1 Intro
  2. 2 Hypersurface Singularities
  3. 3 Properties of the singularity index at point 0 € V()
  4. 4 Is there a smallest possible singularity index?
  5. 5 "Worst" singularity on an irreducible hypersurface?
  6. 6 Cone Singularities and Homogeneous Polynomials Let & be a homogeneous polynomial of degree (in n variables).
  7. 7 Example: Cubic cones of dimension two
  8. 8 Extremal singularities occur ONLY in characteristic p 0.
  9. 9 Classification of Extremal Singularities
  10. 10 Geometry of extremal singularities?
  11. 11 Understanding Geometry of smooth Cubic Surface
  12. 12 Triangles on cubic surfaces
  13. 13 When is the cone over cubic surface extremal singularity?
  14. 14 A similar phenomenon happens in every degreed

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