A bound on the projective dimension of three cubics
نویسنده
چکیده
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.
منابع مشابه
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 whether ideals generated by three cubic forms can have projective dimension greater than four, by constructing one with projective dimension equal to five.
متن کاملOn 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 کاملCharacterization of projective special linear groups in dimension three by their orders and degree patterns
The prime graph $Gamma(G)$ of a group $G$ is a graph with vertex set $pi(G)$, the set of primes dividing the order of $G$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $psim q$ if there is an element in $G$ of order $pq$. Let $pi(G)={p_{1},p_{2},...,p_{k}}$. For $pinpi(G)$, set $deg(p):=|{q inpi(G)| psim q}|$, which is called the degree of $p$. We also set $D(G):...
متن کاملSome Theorems of Comparison and Oscillation
+ S&iX2(Xi — X2)} = 0. Clearly, the quartic degenerates into the #-line of the pencil of cubics, and into a cubic having (si, s2) sz) as the $-point. Hence the THEOREM: Any cubic of the net with a given S-point may be generated by any pencil of cubics within the net, not containing the given cubic, and the projective pencil of lines joining the Spoint of the given cubic to the S-points of the c...
متن کاملGorenstein projective objects in Abelian categories
Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Symb. Comput.
دوره 45 شماره
صفحات -
تاریخ انتشار 2010