Taiwanese Journal of Mathematics

An Application of Liaison Theory to Zero-dimensional Schemes

Martin Kreuzer, Tran N. K. Linh, Le Ngoc Long, and Tu Chanh Nguyen

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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.

Article information

Taiwanese J. Math., Volume 24, Number 3 (2020), 553-573.

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

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Digital Object Identifier

Primary: 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12] 14M06: Linkage [See also 13C40]
Secondary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series 14N05: Projective techniques [See also 51N35]

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


Kreuzer, Martin; Linh, Tran N. K.; Long, Le Ngoc; Nguyen, Tu Chanh. An Application of Liaison Theory to Zero-dimensional Schemes. Taiwanese J. Math. 24 (2020), no. 3, 553--573. doi:10.11650/tjm/190710. https://projecteuclid.org/euclid.twjm/1589875219

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