Mixing
Heuristics for finding minimal primes/ primary decomp. Example: (XZ-Y^2, X^3-YZ)
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In occassions where I need to find the minimal primes associated to an ideal / find a primary decomp., sometimes I can do it just fine, sometimes I find myself completely blind in the search for it.
So Im here asking for general heuristics for this, and also for relevant lemmas and theorems that are frequently used in such situations.
As an example, could someone please explain to me how to find:
- the minimal primes
- a primary decomposition
Of an ideal such as:
$J = ( XZ-Y^2 , X^3-YZ)$ , to be understood inside the polynomial ring in the variables X Y Z over a field k.
Thanks
PS: I already looked for some similar questions on this site, but the ones I found were not very clarifying.
algebraic-geometry polynomials commutative-algebra polynomial-rings primary-decomposition
asked Jan 25 at 14:33
GLeGLe
455
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add a comment |
$begingroup$
In occassions where I need to find the minimal primes associated to an ideal / find a primary decomp., sometimes I can do it just fine, sometimes I find myself completely blind in the search for it.
So Im here asking for general heuristics for this, and also for relevant lemmas and theorems that are frequently used in such situations.
As an example, could someone please explain to me how to find:
- the minimal primes
- a primary decomposition
Of an ideal such as:
$J = ( XZ-Y^2 , X^3-YZ)$ , to be understood inside the polynomial ring in the variables X Y Z over a field k.
Thanks
PS: I already looked for some similar questions on this site, but the ones I found were not very clarifying.
algebraic-geometry polynomials commutative-algebra polynomial-rings primary-decomposition
asked Jan 25 at 14:33
GLeGLe
455
$endgroup$
$begingroup$
I do not know an answer to your question, but finding a primary decomposition is not easy. For instance, link.springer.com/article/10.1007/BF01231331. In some sense, this is one of the advantages of reducing a problem into a problem of monomial ideals, and primary decompositions for monomial ideals are well-known.
$endgroup$
– Youngsu
Jan 25 at 16:50
add a comment |
$begingroup$
In occassions where I need to find the minimal primes associated to an ideal / find a primary decomp., sometimes I can do it just fine, sometimes I find myself completely blind in the search for it.
So Im here asking for general heuristics for this, and also for relevant lemmas and theorems that are frequently used in such situations.
As an example, could someone please explain to me how to find:
- the minimal primes
- a primary decomposition
Of an ideal such as:
$J = ( XZ-Y^2 , X^3-YZ)$ , to be understood inside the polynomial ring in the variables X Y Z over a field k.
Thanks
PS: I already looked for some similar questions on this site, but the ones I found were not very clarifying.
algebraic-geometry polynomials commutative-algebra polynomial-rings primary-decomposition
asked Jan 25 at 14:33
GLeGLe
455
$endgroup$
In occassions where I need to find the minimal primes associated to an ideal / find a primary decomp., sometimes I can do it just fine, sometimes I find myself completely blind in the search for it.
So Im here asking for general heuristics for this, and also for relevant lemmas and theorems that are frequently used in such situations.
As an example, could someone please explain to me how to find:
- the minimal primes
- a primary decomposition
Of an ideal such as:
$J = ( XZ-Y^2 , X^3-YZ)$ , to be understood inside the polynomial ring in the variables X Y Z over a field k.
Thanks
PS: I already looked for some similar questions on this site, but the ones I found were not very clarifying.
algebraic-geometry polynomials commutative-algebra polynomial-rings primary-decomposition
algebraic-geometry polynomials commutative-algebra polynomial-rings primary-decomposition
asked Jan 25 at 14:33
GLeGLe
455
asked Jan 25 at 14:33
GLeGLe
455
edited Jan 26 at 15:22
GLe
asked Jan 25 at 14:33
GLeGLe
455
asked Jan 25 at 14:33
GLeGLe
455
asked Jan 25 at 14:33
GLeGLe
455
455
$begingroup$
I do not know an answer to your question, but finding a primary decomposition is not easy. For instance, link.springer.com/article/10.1007/BF01231331. In some sense, this is one of the advantages of reducing a problem into a problem of monomial ideals, and primary decompositions for monomial ideals are well-known.
$endgroup$
– Youngsu
Jan 25 at 16:50
add a comment |
$begingroup$
I do not know an answer to your question, but finding a primary decomposition is not easy. For instance, link.springer.com/article/10.1007/BF01231331. In some sense, this is one of the advantages of reducing a problem into a problem of monomial ideals, and primary decompositions for monomial ideals are well-known.
$endgroup$
– Youngsu
Jan 25 at 16:50
$begingroup$
I do not know an answer to your question, but finding a primary decomposition is not easy. For instance, link.springer.com/article/10.1007/BF01231331. In some sense, this is one of the advantages of reducing a problem into a problem of monomial ideals, and primary decompositions for monomial ideals are well-known.
$endgroup$
– Youngsu
Jan 25 at 16:50
$begingroup$
I do not know an answer to your question, but finding a primary decomposition is not easy. For instance, link.springer.com/article/10.1007/BF01231331. In some sense, this is one of the advantages of reducing a problem into a problem of monomial ideals, and primary decompositions for monomial ideals are well-known.
$endgroup$
– Youngsu
Jan 25 at 16:50
add a comment |
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$begingroup$
I do not know an answer to your question, but finding a primary decomposition is not easy. For instance, link.springer.com/article/10.1007/BF01231331. In some sense, this is one of the advantages of reducing a problem into a problem of monomial ideals, and primary decompositions for monomial ideals are well-known.
$endgroup$
– Youngsu
Jan 25 at 16:50