Enumeration of curves with two singular points
نویسندگان
چکیده
منابع مشابه
On the enumeration of complex plane curves with two singular points
We study equi-singular strata of curves with two singular points of prescribed types. The method of our previous work [Kerner04] is generalized to this case. This allows to solve the enumerative problem for plane curves with two singular points of linear singularity types. In the general case this reduces the enumerative questions to the problem of collision of the two singular points. The meth...
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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.
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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...
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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 ...
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This is an extended, renovated and updated report on our joint work [OZ]. The main result is an inequality for the numerical type of singularities of a plane curve, which involves the degree of the curve, the multiplicities and the Milnor numbers of its singular points. It is a corollary of the logarithmic Bogomolov-Miyaoka-Yau's type inequality due to Miyaoka. It was first proven by F. Sakai a...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2015
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2014.11.006