奇异列维平面超曲面的回拉

IF 0.8 4区数学 Q2 MATHEMATICS Arkiv for Matematik Pub Date : 2021-07-02 DOI:10.4310/arkiv.2021.v59.n2.a3

A. Beltr'an, A. Fern'andez-P'erez, Hern'an Neciosup

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引用次数: 0

摘要

．利用复射影空间中的奇异全纯叶研究了奇异实解析列维平面子集的不变性。给出了实解析列维平坦子集在有理映射下是复射影曲面上半解析列维平坦超曲面的回拉或在亚纯函数下是实代数曲线的回拉的充分条件。特别地，我们给出了奇异实解析列维平坦超曲面的一个应用。由于Lebl和Bretas-Fernández-Pérez-Mol，我们的结果改进了以前的结果。

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Pull-back of singular Levi-flat hypersurfaces

. We study singular real analytic Levi-ﬂat subsets invariant by singular holomorphic foliations in complex projective spaces. We give suﬃcient conditions for a real analytic Levi-ﬂat subset to be the pull-back of a semianalytic Levi-ﬂat hypersurface in a complex projective surface under a rational map or to be the pull-back of a real algebraic curve under a meromorphic function. In particular, we give an application to the case of a singular real analytic Levi-ﬂat hypersurface. Our results improve previous ones due to Lebl and Bretas–Fernández-Pérez–Mol.

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