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http://dx.doi.org/10.4134/BKMS.b210544

THE KÄHLER DIFFERENT OF A SET OF POINTS IN ℙm × ℙn  

Hoa, Nguyen T. (Department of Mathematics University of Education Hue University)
Linh, Tran N.K. (Department of Mathematics University of Education Hue University)
Long, Le N. (Fakultat fur Informatik und Mathematik Universitat Passau and Department of Mathematics University of Education Hue University)
Nhan, Phan T.T. (Department of Mathematics University of Education Hue University)
Nhi, Nguyen T.P. (Department of Mathematics University of Education Hue University)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.4, 2022 , pp. 929-949 More about this Journal
Abstract
Given an ACM set 𝕏 of points in a multiprojective space ℙm×ℙn over a field of characteristic zero, we are interested in studying the Kähler different and the Cayley-Bacharach property for 𝕏. In ℙ1×ℙ1, the Cayley-Bacharach property agrees with the complete intersection property and it is characterized by using the Kähler different. However, this result fails to hold in ℙm×ℙn for n > 1 or m > 1. In this paper we start an investigation of the Kähler different and its Hilbert function and then prove that 𝕏 is a complete intersection of type (d1, …, dm, d'1, …, d'n) if and only if it has the Cayley-Bacharach property and the Kähler different is non-zero at a certain degree. We characterize the Cayley-Bacharach property of 𝕏 under certain assumptions.
Keywords
ACM set of points; complete intersection; Cayley-Bacharach property; Kahler different;
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