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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제59권 제4호
- 발행연도
- 2022.7
- 수록면
- 929 - 949 (21page)
- DOI
- 10.4134/BKMS.b210544
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Given an ACM set $\X$ of points in a multiprojective space $\pmpn$ over a field of characteristic zero, we are interested in studying the K\"ahler different and the Cayley-Bacharach property for $\X$. In $\bbP^1\times \bbP^1$, the Cayley-Bacharach property agrees with the complete intersection property and it is characterized by using the K\"ahler different. However, this result fails to hold in $\pmpn$ for $n>1$ or $m>1$. In this paper we start an investigation of the K\"ahler different and its Hilbert function and then prove that $\X$ is a complete intersection of type $(d_1,\ldots,d_m,d'_1,\ldots,d'_n)$ if and only if it has the Cayley-Bacharach property and the K\"ahler different is non-zero at a certain degree. We characterize the Cayley-Bacharach property of $\X$ under certain assumptions.
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