The Classification of Singular Points of Algebraic Curves
نویسندگان
چکیده
منابع مشابه
Non-singular Points on Algebraic Curves and Codimension-1 primes
Let K be a perfect field and K be a fixed algebraic closure of K. We begin our study of algebraic geometry with affine n-space and its subsets defined by zeros of polynomials.
متن کاملEnumeration of singular algebraic curves
We enumerate plane algebraic curves with one singular point of any (prescribed) singularity type. It is shown how to generalize the method to the singular hypersurfaces and some cases of enumeration of singular hypersurfaces are solved.
متن کاملSingular Points of Plane Curves
ly isomorphic to (C×)r−1 × (C), and hence also to (S1)r−1 × (R), where r = |J | is the number of branches and k = δ(C)− r+1 = 1 2 (μ(C) + 1 − r). The construction of the Jacobian variety J(C̃) of the non-singular curve C̃ in the large is standard in algebraic geometry. There is also a notion of Jacobian of a singular curve C , defined e.g. in [85], which, like the other, is an abelian group. Ther...
متن کاملOn the collisions of singular points of complex algebraic plane curves
We study the ”generic” degenerations of curves with two singular points when the points merge. First, the notion of generic degeneration is defined precisely. Then a method to classify the possible results of generic degenerations is proposed in the case of linear singularity types. We discuss possible bounds on the singularity invariants of the resulting type in terms of the initial types. In ...
متن کاملComputing singular points of plane rational curves
We compute the singular points of a plane rational curve, parametrically given, using the implicitization matrix derived from the μ-basis of the curve. It is shown that singularity factors, which are defined and uniquely determined by the elementary divisors of the implicitization matrix, contain all the information about the singular points, such as the parameter values of the singular points ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1965
ISSN: 0002-9947
DOI: 10.2307/1993972