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Results tagged with ac.commutative-algebra
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user 70593
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
4
votes
1
answer
250
views
Can relative flatness of a sheaf be tested using (faithfully) flat morphisms?
Given a $\mathbb{C}$-scheme $S$, two $S$-schemes $X$ and $Y$ that are flat over $S$ and a coherent sheaf of $O_Y$-modules $F$.
Assume we have a (faithfully) flat $S$-morphism $\pi: X \rightarrow Y$ a …
- 1,025
3
votes
0
answers
327
views
Which sheaves on a projective bundle are flat over the base scheme?
Assume $X$ is a noetherian scheme over $\mathbb{C}$ and $E$ a locally free sheaf of finite rank on $X$. Denote the the associated projective bundle by $f: \mathbb{P}(E)\rightarrow X$.
Are there any c …
- 1,025
0
votes
1
answer
109
views
How to find ideals of finite length in a power series ring with special properties?
Let $A$ be the power series ring $\mathbb{C}[[x,y]]$.
Assume we are given two ideals $I,J$ of finite length in $A$ such that:
$xJ\subseteq I\subseteq J$
Is it possible to find ideals of finite le …
- 1,025
0
votes
0
answers
80
views
A quaternion x generates a left ideal of rank 2 if and only if x, ix and jx are linearly dep...
I am trying to understand the construction of Artin and Mumford of a non-rational unirational threefold in ([1], p.90).
Assume $S$ is a smooth projective surface over $\mathbb{C}$ with a smooth curv …
- 1,025