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摘要翻译：
多项式几何中的Marden定理和二次曲线射影几何中的大Poncelet定理以其古典美而占有非常特殊的地位。我们的主要目的是在这两个定理之间呈现出一种强有力的、意想不到的关系。我们建立了完全Marden定理和Poncelet-Darboux定理之间的动力学等价。通过引入一类{It等焦变形}，我们构造了Marden曲线与Poncelet-Darboux曲线之间的态射。在此基础上，利用定义了一条次为$n-1$的Poncelet-Darboux曲线的多项式对，给出了当$n$为奇数时，该曲线在$(n-1)/2$二次曲线上完全分解的有效判据；如果$n$是偶数，则完全分解由$(n-2)/2$圆锥曲线和一条线组成。这是研究特殊而非hooft的瞬子束的一个重要问题。
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英文标题：
《Marden theorem and Poncelet-Darboux curves》
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作者：
Vladimir Dragovic
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Classical Analysis and ODEs 经典分析与颂歌
分类描述：Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
特殊函数、正交多项式、调和分析、Ode、微分关系、变分法、逼近、展开、渐近
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
The Marden theorem of geometry of polynomials and the great Poncelet theorem from projective geometry of conics by their classical beauty occupy very special places. Our main aim is to present a strong and unexpected relationship between the two theorems. We establish a dynamical equivalence between the full Marden theorem and the Poncelet-Darboux theorem. By introducing a class of {\it isofocal deformations}, we construct morphisms between the Marden curves and the Poncelet-Darboux curves. Then we present effective criterion in terms of pair of polynomials which defines a Poncelet-Darboux curve of degree $n-1$, for complete decomposition of the curve on $(n-1)/2$ conics if $n$ is odd; if $n$ is even, complete decomposition consists of $(n-2)/2$ conics and a line. This is an important question in the study of special, 'tHooft, instanton bundles.
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PDF链接：
https://arxiv.org/pdf/0812.4829
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