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摘要翻译：
我们计算了阶为n$的Poncelet曲线的投影变化的阶。该变体是维数$2n+5$的不可约变体，位于度$n$平面曲线的射影空间内。经典的定义是通过光滑二次曲线（二次曲线和二次曲线都是可变的）内接的非退化的n$边多边形的顶点的局部闭曲线子集在该射影空间上的闭包。它与射影（对偶）平面上一类特殊的半稳定滑轮有关，称为Poncelet滑轮。利用对Poncelet曲线变化的模空间，计算求取度。它涉及到相当繁琐的计算，我们得到了$n\geq4$的一般公式。我们做了$n\leq6$的数值应用。当$n=4$时，我们得到了射影平面的Donaldson数54,它是Luroth四元超曲面的次。
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英文标题：
《Le degre de la variete des courbes de Poncelet》
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作者：
Yann Sepulcre
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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 compute the degree of the projective variety of Poncelet curves of degree $n$. This variety is irreducible of dimension $2 n + 5$, and lies inside the projective space of degree $n$ plane curves. It is classically defined as the closure on this projective space of the locally closed subset of curves passing through the vertices of some nondegenerate $n$ sided polygone inscribed in some smooth conic (the polygone and the conic being variable). It is related to a specific class of semi-stable sheaves on the projective (dual) plane, named Poncelet sheaves. Using moduli spaces birational to the variety of Poncelet curves, we compute the requested degree. It involves quite cumbersome computations, and we obtain general formulas for $n \geq 4$. We do numerical applications for $n \leq 6$. For $n=4$ we find back the well known Donaldson number of the projective plane, 54, which is the degree of the hypersurface of Luroth quartics.
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PDF链接：
https://arxiv.org/pdf/0709.1334
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