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Results tagged with ac.commutative-algebra
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user 48585
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
4
votes
Symmetric algebra of an ideal and syzygies
Quite in general, let $M$ be an $R$-module represented as the cockernel of a linear map $f: G\to F$ of free R-moduels $F$ and $G$ of rank $n$ and $m$. Then $\text{Sym}(M)$ is isomorphic (as an R-algeb …
- 151
3
votes
Accepted
When two determinantal ideals together generate a power of the maximal ideal?
Let me discuss the graded case, that is the ring is the polynomial ring and the matrices have general homogeneous entries of degree $1$. The local version should follows by taking "lowest order part" …
- 151
3
votes
Accepted
Theorem 2.5 in "Castelnuovo-Mumford regularity of products of ideals" by Conca & Herzog
The point is that if the base field is infinite (as one can assume after a field extension) a general enough linear form is almost regular. This follows from the so called prime avoidance.
- 151
2
votes
How to find the generic initial ideal?
The general problem of computing invariants of the lexicographic generic initial ideal of an ideal is discussed in the last chapter of Mark Green Barcelona's notes
There are papers devoted in particu …
- 151
0
votes
Castelnuovo-Mumford Regularity of Ideals of Maximal Minors
One possible explanation for what you are claiming is that the ideal of m-minors is equal to the m-th power of the maximal ideal (x,y,z,w). Did you check if this is the case?
- 151
0
votes
Arithmetic Cohen-Macaulayness of curves/surfaces defined by weighted power sums in 3 variables
I do not know if it is related to your problems, but there are two papers of R. Dvornicich and U. Zannier studying the field of fraction generated by subsets of the P_i in the case p,q and r are equal …
- 151
0
votes
When is a power of an indeterminate in an ideal with 2 generators?
Do you assume the ideal is homogeneous? No power of $S$ belong to $(X,S-1)$.
If you assume that the ideal is homogeneous, then $S^m$ is in the ideal $(f,g)$ for $m=\deg f+\deg g-1$. Indeed all homog …
- 151