• 대한수학회보
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• 제61권4호
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• pp.1067-1086
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• 2024

For a foliation 𝓕 of degree r over ℙ², we can regard it as a maximal invertible sheaf N^∨_𝓕 of Ω_ℙ², which is represented by a section s ∈ H⁰(Ω_ℙ² (r+2)). The singular locus Sing𝓕 of 𝓕 is the zero dimensional subscheme Z(s) of ℙ² defined by s. Campillo and Olivares have given some characterizations of the singular locus by using some cohomology groups. In this paper, we will give some different characterizations. For example, the singular locus of a foliation over ℙ² can be characterized as the residual subscheme of r collinear points in a complete intersection of two curves of degree r + 1.