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摘要翻译：
从代数几何的角度研究了代数曲线上的锥面，分析了它们的主要代数性质。利用关联图给出了代数曲线扇形的形式定义。我们证明了除以焦点为中心以$d$为半径的圆外，贝壳线是一条至多有两个不可约分量的代数曲线。此外，我们还引入了贝类的特殊成分和简单成分的概念。此外，我们还指出，除了通过焦点的线之外，贝壳线总是至少有一个简单的分量，并且对于几乎每一个距离，贝壳线的所有分量都是简单的。我们指出，在可约的情况下，简单的扇形分量与初始曲线是双形等价的，并且我们证明了如何用特殊的分量来判断一条给定的代数曲线是否是另一条曲线的扇形。
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英文标题：
《An Algebraic Analysis of Conchoids to Algebraic Curves》
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作者：
J. Rafael Sendra, Juana Sendra
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最新提交年份：
2007
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分类信息：
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：
We study conchoids to algebraic curve from the perspective of algebraic geometry, analyzing their main algebraic properties. We introduce the formal definition of conchoid of an algebraic curve by means of incidence diagrams. We prove that, with the exception of a circle centered at the focus and taking $d$ as its radius, the conchoid is an algebraic curve having at most two irreducible components. In addition, we introduce the notions of special and simple components of a conchoid. Moreover we state that, with the exception of lines passing through the focus, the conchoid always has at least one simple component and that, for almost every distance, all the components of the conchoid are simple. We state that, in the reducible case, simple conchoid components are birationally equivalent to the initial curve, and we show how special components can be used to decide whether a given algebraic curve is the conchoid of another curve.
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PDF链接：
https://arxiv.org/pdf/0705.4590
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