Algebraic geometry for scientists and engineers
Algebraic geometry for scientists and engineers
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DOI：
10.1090/surv/035
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
S. Abhyankar
中科院分区：
文献类型：
--
作者：
S. Abhyankar
有理和多项式参数化分数线性变换三次曲线三次曲面和一般超曲面平面曲线理论概述仿射平面和射影平面带把手的球面曲线上的函数和微分多项式和幂级数抽象代数复习一些交换代数Hensel引理和牛顿定理更多关于牛顿定理分支和赋值函数和微分的除数Weierstrass预备定理相交重数平面曲线奇异点的解析解在奇异点附近不间断参数化具有三个双点的四次曲线特征对一个位置和雅可比问题的准则反演公式和雅可比问题曲面超曲面代数曲面奇异点的解析解双有理和多有理变换赋值和双有理对应通过各种结式的有理圆柱。
Rational and polynomial parametrizations Fractional linear transformations Cubic curves Cubic surfaces and general hypersurfaces Outline of the theory of plane curves Affine plane and projective plane Sphere with handles Functions and differentials on a curve Polynomials and power series Review of abstract algebra Some commutative algebra Hensel's lemma and Newton's theorem More about Newton's theorem Branches and valuations Divisors of functions and differentials Weierstrass preparation theorem Intersection multiplicity Resolution of singularities of plane curves Infinitely near singularities Parametrizing a quartic with three double points Characteristic pairs Criterion for one place and Jacobian problem Inversion formula and Jacobian problem Surfaces Hypersurfaces Resolution of singularities of algebraic surfaces Birational and polyrational transformations Valuations and birational correspondence Rational cylinders through a variety Resultants.