CONTENTS -- NEWTON POLYHEDRA WITHOUT COORDINATES -- 1. Introduction -- Chapter 1. Integrally closed filtrations -- 2. Definition and examples -- 3. The language of integrally closed subalgebras -- 4. Generators of a filtration -- 5. Join and suspension -- 6. Normal crossing rings and monomials -- 7. Special filtrations and the Main Theorem -- Chapter 2. Contact and stably contact filtrations -- 8. Initial forms and transversality to the normal crossing divisor -- 9. Contact filtrations and their structure -- 10. Galois extensions
21. Some unsolved problemsAppendices -- A1. Weights of a quasihomogeneous filtration are independent of the coordinate system -- A2. Criterion for integral closedness -- A3. The structure of suspension -- A4. Multiplication and division by monomials: Proof of the structure theorem -- A5. Suspension of a stably contact filtration is stably contact: Proof of (11.5) -- References -- NEWTON POLYHEDRA OF IDEALS -- 1. Introduction -- 2. Standard bases and the main result -- 3. Differential operators and principal parts -- 4. Generalized Fitting ideals
5. Heuristics6. 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 -- References
Bibliography
Includes bibliographical references at the end of each chapters
