1,003 research outputs found
On the projective dimension and the unmixed part of three cubics
Let be a polynomial ring over a field in an unspecified number of
variables. We prove that if is an ideal generated by three cubic
forms, and the unmixed part of contains a quadric, then the projective
dimension of is at most 4. To this end, we show that if is
a three-generated ideal of height two and an ideal linked to the
unmixed part of , then the projective dimension of is bounded above by
the projective dimension of plus one.Comment: 23 pages; to appear in Journal of Algebr
Local rings of countable Cohen--Macaulay type
We prove (the excellent case of) Schreyer's conjecture that a local ring with
countable Cohen--Macaulay type has at most a one-dimensional singular locus.
Furthermore we prove that the localization of a Cohen-Macaulay local ring of
countable CM type is again of countable CM type.Comment: 6 page
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