Titlebook: Introduction to Plane Algebraic Curves; Ernst Kunz Textbook 2005 Birkhäuser Boston 2005 Algebraic curve.Belshoff.Kunz.algebra.computer alg

分离

TAIN

Regular and Singular Points of Algebraic Curves. Tangentsmultiplicity” that indicates how many times it has to be counted as a point of the curve. The “tangents” of a curve will also be explained.One can decide whether a point is simple or singular with the help of the local ring at the point.The facts from Appendix E on Noetherian rings and discrete valu

2否定

Rational Maps. Parametric Representations of Curves birational equivalence by rational maps.It will also be shown that a curve is rational precisely when it has a “parametric representation.” This chapter depends on Chapter 4, but it also uses parts of Chapter 6.

使厌恶

Elliptic Curveshmetic (Husemöller [Hus], Lang [L], Silverman [S.], [S.]). On the role of elliptic curves in cryptography, see Koblitz [K] and Washington [W]. After choosing a point O,an elliptic curve may be given a group structure using a geometric construction. We first concern ourselves with this construction.

Pruritus

Residue Calculusential form ω =.). They generalize the intersection multiplicity of two curves in a certain sense, and they contain more precise information about the intersection behavior. The elementary and purely algebraic construction of the residue that we present here is based on Appendix H and goes back to S

后退

Applications of Residue Theory to Curvesion theory of plane curves. Maybe B. Segre [.] was the first who proceeded in a way similar to ours, but he used another concept of residue, the residue of differentials on a smooth curve. See also Griffiths-Harris [.], Chapter V. The theorems presented here have far-reaching higher-dimensional gene

致命

The Riemann-Roch Theoremrs at the points on the curves (or on the abstract Riemann surface ). Using the methods of Appendix L we will derive two versions of the Riemann-Roch theorem, one for the curve itself and one for its Riemann surface (its function field). The theorem leads to an important birational invariant of irre

Moderate

成绩上升

The Branches of a Curve Singularityof decomposing curves into “analytic” branches “in a neighborhood” of a singularity,and thereby allowing us to analyze them more precisely. Also, a similar theory will be discussed for curves over an arbitrary algebraically closed field.

Germinate

Conductor and Value Semigroup of a Curve Singularity“ranches,” and “intersection multiplicity between the branches,” to the conductor and value semigroup. This will allow a more precise classification of curve singularities than was possible up to now. Also, we will be led to other formulas for calculating the genus of the function field of a curve.