度数为 2 的ℂℙ2 上全形叶形的 GIT 商和四元平面曲线

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-08-04 DOI:10.1515/forum-2024-0043

Claudia R. Alcántara, Juan Vásquez Aquino

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引用次数: 0

摘要

我们研究的是ℂ ℙ 2 上{\mathbb{CP}^{2}}度为 2 且坐标不变的叶状空间的商变种。我们找到了这一曲面的交点贝蒂数。推论是，这些交集贝蒂数与四元平面曲线商综的交集贝蒂数重合。最后，我们给出了具有不同奇异点且无不变线的 2 度叶形空间与光滑四元平面曲线空间之间的明确同构关系。

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GIT quotient of holomorphic foliations on ℂℙ2 of degree 2 and quartic plane curves

We study the quotient variety of the space of foliations on ℂ ⁢ ℙ 2

{\mathbb{CP}^{2}}

of degree 2 up to change of coordinates. We find the intersection Betti numbers of this variety. As a corollary, we have that these intersection Betti numbers coincide with the intersection Betti numbers of the quotient variety of quartic plane curves. Finally, we give an explicit isomorphism between the space of foliations of degree 2 with different singular points, without invariant lines and the space of smooth quartic plane curves.

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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.