Hypersurfaces with many Aj-singularities: Explicit constructions
نویسندگان
چکیده
منابع مشابه
DESSINS D’ENFANTS AND HYPERSURFACES WITH MANY Aj-SINGULARITIES OLIVER LABS
We show the existence of surfaces of degree d in È 3 () with approximately 3j+2 6j(j+1) d 3 singularities of type A j , 2 ≤ j ≤ d − 1. The result is based on Chmutov's construction of nodal surfaces. For the proof we use plane trees related to the theory of Dessins d'Enfants. Our examples improve the previously known lower bounds for the maximum number µ A j (d) of A j-singularities on a surfac...
متن کاملDESSINS D’ENFANTS AND HYPERSURFACES WITH MANY Aj-SINGULARITIES OLIVER LABS
We show the existence of surfaces of degree d in È 3 () with approximately 3j+2 6j(j+1) d 3 singularities of type A j , 2 ≤ j ≤ d − 1. The result is based on Chmutov's construction of nodal surfaces. For the proof we use plane trees related to the theory of Dessins d'Enfants. Our examples improve the previously known lower bounds for the maximum number µ A j (d) of A j-singularities on a surfac...
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In [7] we have shown that special types of simplicial arrangements of d lines contain simple arrangements which are related to a class of bivariate polynomials Jd(x,y) having many critical points with few critical values. The polynomials have been used in the construction of algebraic surfaces with many A and D singularities [4, 5, 6, 7]. Tilings exhibiting non crystallographic symmetries have ...
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The calculus of constructions can be extended with an infinite hierarchy of universes and cumulative subtyping. Subtyping is usually left implicit in the typing rules. We present an alternative version of the calculus of constructions where subtyping is explicit. We avoid problems related to coercions and dependent types by using the Tarski style of universes and by adding equations to reflect ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2014
ISSN: 0377-0427
DOI: 10.1016/j.cam.2013.03.045