# Algebraic Geometry for Scientists and Engineers

### About this Title

**Shreeram S. Abhyankar**

Publication: Mathematical Surveys and Monographs

Publication Year
1990: Volume 35

ISBNs: 978-0-8218-1535-9 (print); 978-1-4704-1262-3 (online)

DOI: http://dx.doi.org/10.1090/surv/035

MathSciNet review: MR1075991

MSC: Primary 14-01; Secondary 00A06

### Table of Contents

**Front/Back Matter**

**Chapters**

- Lecture 1. Rational and polynomial parametrizations
- Lecture 2. Fractional linear transformations
- Lecture 3. Cubic curves
- Lecture 4. Cubic surfaces and general hypersurfaces
- Lecture 5. Outline of the theory of plane curves
- Lecture 6. Affine plane and projective plane
- Lecture 7. Sphere with handles
- Lecture 8. Functions and differentials on a curve
- Lecture 9. Polynomials and power series
- Lecture 10. Review of abstract algebra
- Lecture 11. Some commutative algebra
- Lecture 12. Hensel’s lemma and Newton’s theorem
- Lecture 13. More about Newton’s theorem
- Lecture 14. Branches and valuations
- Lecture 15. Divisors of functions and differentials
- Lecture 16. Weierstrass preparation theorem
- Lecture 17. Intersection multiplicity
- Lecture 18. Resolution of singularities of plane curves
- Lecture 19. Infinitely near singularities
- Lecture 20. Parametrizing a quartic with three double points
- Lecture 21. Characteristic pairs
- Lecture 22. Criterion for one place and Jacobian problem
- Lecture 23. Inversion formula and Jacobian problem
- Lecture 24. Surfaces
- Lecture 25. Hypersurfaces
- Lecture 26. Resolution of singularities of algebraic surfaces
- Lecture 27. Birational and polyrational transformations
- Lecture 28. Valuations and birational correspondence
- Lecture 29. Rational cylinders through a variety
- Lecture 30. Resultants