分离
发表于 2025-3-25 04:58:35
http://reply.papertrans.cn/48/4741/474039/474039_21.png
TAIN
发表于 2025-3-25 08:57:54
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
发表于 2025-3-25 12:28:35
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
发表于 2025-3-25 19:33:10
Elliptic Curveshmetic (Husemöller , Lang , Silverman , ). On the role of elliptic curves in cryptography, see Koblitz and Washington . 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
发表于 2025-3-25 23:40:23
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
发表于 2025-3-26 04:02:39
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
发表于 2025-3-26 06:26:16
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
发表于 2025-3-26 11:49:31
http://reply.papertrans.cn/48/4741/474039/474039_28.png
成绩上升
发表于 2025-3-26 14:11:35
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
发表于 2025-3-26 19:09:44
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.