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June, 2020 An Application of Liaison Theory to Zero-dimensional Schemes
Martin Kreuzer, Tran N. K. Linh, Le Ngoc Long, Tu Chanh Nguyen
Taiwanese J. Math. 24(3): 553-573 (June, 2020). DOI: 10.11650/tjm/190710


Given a $0$-dimensional scheme $\mathbb{X}$ in an $n$-dimensional projective space $\mathbb{P}^n_K$ over an arbitrary field $K$, we use liaison theory to characterize the Cayley-Bacharach property of $\mathbb{X}$. Our result extends the result for sets of $K$-rational points given in [8]. In addition, we examine and bound the Hilbert function and regularity index of the Dedekind different of $\mathbb{X}$ when $\mathbb{X}$ has the Cayley-Bacharach property.


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Martin Kreuzer. Tran N. K. Linh. Le Ngoc Long. Tu Chanh Nguyen. "An Application of Liaison Theory to Zero-dimensional Schemes." Taiwanese J. Math. 24 (3) 553 - 573, June, 2020.


Received: 6 December 2018; Revised: 8 July 2019; Accepted: 30 July 2019; Published: June, 2020
First available in Project Euclid: 19 May 2020

zbMATH: 07251187
MathSciNet: MR4100709
Digital Object Identifier: 10.11650/tjm/190710

Primary: 13C40 , 14M06
Secondary: 13D40 , 14N05

Keywords: Cayley-Bacharach property , Dedekind different , Hilbert function , liaison theory , zero-dimensional scheme

Rights: Copyright © 2020 The Mathematical Society of the Republic of China


Vol.24 • No. 3 • June, 2020
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