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Results tagged with ag.algebraic-geometry
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user 23950
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
5
votes
1
answer
438
views
Macaulay's example of prime ideals in $\mathbb C[X_1,X_2,X_3]$ having large number of genera...
There is a famous example of Macaulay which shows that there are prime ideals of height two in $\mathbb C[X_1,X_2,X_3]$ having at least $l$ generators for any $l\ge 3$.
In Macaulay's words, the exam …
- 1,313
3
votes
Is a Laskerian ring coherent
Even strongly Laskerian rings are not necessarily coherent.
By a theorem of Radu strongly Laskerian coherent rings are Noetherian, and there are examples of strongly Laskerian rings which are not No …
- 1,313
2
votes
Accepted
If the quotient of a local ring is regular, does that imply that the original ring must be r...
The quoted result relies on the following elementary characterization of local regular rings:
Let $R$ be a local ring with maximal ideal $\mathfrak m$ and $x\in\mathfrak m-\mathfrak m^2$. Then $R$ …
- 1,313
1
vote
transcendence degree of subring of polynomial ring
Set $R=k[p_1,\dots,p_t]$, $S=k[x_1,\dots,x_r]$ and $\mathfrak{m}=(x_1,\dots,x_r)$ (the maximal irrelevant ideal of $S$). We know that the ideal $(p_1,\dots,p_t)S$ is $\mathfrak{m}$-primary. A graded v …
- 1,313