In this article we focus on the study of special parabolic points in surfaces arising as graphs of polynomials, we prove that Viro’s construction glues a class of special parabolic points that we call transversal and build families of real polynomials in two variables with a prescribed number of special parabolic points in their graphs. When $$13\le d\le $$ 13 ≤ d ≤ 10,000, we use this result to build a family of degree d real polynomials in two variables with $$(d-4)(2d-9)$$ ( d - 4 ) ( 2 d - 9 ) special parabolic points in its graph. This brings the number of special parabolic points closer to the upper bound of $$(d-2)(5d-12)$$ ( d - 2 ) ( 5 d - 12 ) which is the best known up until now.

中文翻译：

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Viro拼凑得到的多项式图中的横向特殊抛物线点

在本文中，我们重点研究作为多项式图出现的曲面中的特殊抛物线点，我们证明 Viro 的构造将一类特殊抛物线点粘合在一起，我们称之为横向，并在两个变量中建立了具有规定数量的实多项式的族图中的特殊抛物线点。当 $$13\le d\le $$ 13 ≤ d ≤ 10,000 时，我们使用这个结果在两个变量中构建一个 d 次实多项式族，其中 $$(d-4)(2d-9)$$ ( d - 4 ) ( 2 d - 9 ) 其图中的特殊抛物线点。这使得特殊抛物线点的数量更接近 $$(d-2)(5d-12)$$ ( d - 2 ) ( 5 d - 12 ) 的上限，这是迄今为止最著名的。