On the projective dimension and the unmixed part of three cubics
نویسندگان
چکیده
منابع مشابه
On the projective dimension and the unmixed part of three cubics∗
Let R be a polynomial ring over a field in an unspecified number of variables. We prove that if J ⊂ R is an ideal generated by three cubic forms, and the unmixed part of J contains a quadric, then the projective dimension of R/J is at most 4. To this end, we show that if K ⊂ R is a three-generated ideal of height two and L ⊂ R an ideal linked to the unmixed part of K, then the projective dimens...
متن کاملA 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.
متن کاملBound 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 whether ideals generated by three cubic forms can have projective dimension greater than four, by constructing one with projective dimension equal to five.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.11.018