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Newton polyhedra of ideals

About this Title

Boris Youssin

Publication: Memoirs of the American Mathematical Society
Publication Year: 1990; Volume 87, Number 433
ISBNs: 978-0-8218-2495-5 (print); 978-1-4704-0856-5 (online)
DOI: https://doi.org/10.1090/memo/0433
MathSciNet review: 1013092
MSC: Primary 32S10; Secondary 14B05, 14M25

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Table of Contents

Chapters

  • Newton polyhedra without coordinates
  • Introduction
  • 1. Integrally closed filtrations
  • 2. Contact and stably contact filtrations
  • 3. The first derived filtration and its structure
  • 4. Change of the subring
  • Conclusion
  • Appendices
  • Newton polyhedra of ideals
  • 1. Introduction
  • 2. Standard bases and the main result
  • 3. Differential operators and principal parts
  • 4. Generalized Fitting ideals
  • 5. Heuristics
  • 6. Generic position
  • 7. Fitting ideals and filtrations generated by standard bases
  • 8. Normalized standard bases
  • 9. Proof of the Main Theorem 2.7
  • Appendix. Sketch of another proof