Bound on the projective dimension of three cubics

Details Bound on the projective dimension of three cubics Bound on the projective dimension of three cubics

2009-07-10

arxiv.org/abs/0907.1703v1

Journal of Symbolic Computation 45 (2010), 60-73

Mathematics

Commutative Algebra

to appear in Journal of Symbolic Computation

Scientific paper

10.1016/j.jsc.2009.06.005

We show that given any polynomial ring R over a field, and any ideal J in R
which is generated by three cubic forms, the projective dimension of R/J is at
most 36. We also settle the question whether ideals generated by three cubic
forms can have projective dimension greater than 4, by constructing one with
projective dimension equal to 5.

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