An application of Liaison theory to zero-dimensional schemes

2019/04/01 by Martin Kreuzer, Tran N. K. Linh, Kreuzer, Martin +5 · 1 citation
Mathematics · #13C40 #13D40 #14M06 #14N05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C40 #msc:13D40 #msc:14M06 #msc:14N05

paper · pdf · doi:10.48550/arxiv.1904.00703

arxiv created 2019/04/01 · arxiv updated 2019/04/02

Abstract

Given a 0-dimensional scheme X in a n-dimensional projective space Pⁿ_K over an arbitrary field K, we use Liaison theory to characterize the Cayley-Bacharach property of X. Our result extends the result for sets of K-rational points given in [7]. In addition, we examine and bound the Hilbert function and regularity index of the Dedekind different of X when X has the Cayley-Bacharach property.

Cited by

• The Cayley-Bacharach property and the Levinson-Ullery conjecture

Related

• On the Dedekind different of a Cayley-Bacharach scheme
• The Kähler different of a 0-dimensional scheme
• A Cayley-Bacharach theorem and plane configurations
• On the Cayley-Bacharach Property
• Liaison and Castelnuovo-Mumford regularity