AN ARTINIAN QUOTIENT OF THE COORDINATE RING OF A COMPLETE INTERSECTION IN P-n HAVING THE WEAK LEFSCHETZ PROPERTY

作者：Ahn Jeaman; Park Jung Pil^*; Shin Yong Su

来源：Communications in Algebra, 2014, 42(9): 4002-4020.

DOI：10.1080/00927872.2013.804527

• AI-sequence
• Generic initial ideal
• Gorenstein sequence
• Hilbert function
• h-vector
• Unimodal
• Weak Lefschetz property
• Primary: 13A02
• Secondary: 16W50

For a complete intersection set Z = X boolean OR Y of points in a projective space P-n over an algebraically closed field, we prove that the h-vector of the graded Artinian ring R/(I-x+I-Y) is an SI-sequence provided X is also a complete intersection subset of Z and Y=Z\X. Furthermore, we also show that if {X, Y} is a regular division of a general basic configuration Z in P-n, then R/(I-X+I-Y) has the Weak Lefschetz property. These two results give positive answers to the interesting question of [39].

• 出版日期2014-9-2