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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.7
- 수록면
- 1,067 - 1,086 (20page)
- DOI
- 10.4134/BKMS.b230611
이용수
초록· 키워드
오류제보하기
For a foliation $\mathcal{F}$ of degree $r$ over $\mathbb{P}^2$, we can regard it as a maximal invertible sheaf $N_{\mathcal{F}}^{\vee}$ of $\Omega_{\mathbb{P}^2}$, which is represented by a section $s\in H^0(\Omega_{\mathbb{P}^2}(r+2))$. The singular locus ${\rm Sing}\cF$ of $\cF$ is the zero dimensional subscheme $Z(s)$ of $\mathbb{P}^2$ 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 $\mathbb{P}^2$ can be characterized as the residual subscheme of $r$ collinear points in a complete intersection of two curves of degree $r+1$.
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