A bound on the projective dimension of three cubics

We show that given any polynomial ring R over a field and any ideal J R which is generated by three cubic forms, the projective dimension of R/J is at most 36. We also settle the question of whether ideals generated by three cubic forms can have projective dimension greater than four, by constructing one with projective dimension equal to five. Key words: projective dimension, free resolution, unmixed part, linkage

• Type: Journal
• Year: 2010
• Where: JSC
• Authors: Bahman Engheta
• Keywords: Cubic Forms, JSC 2010, Polynomial Ring, Projective Dimension