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Results tagged with ac.commutative-algebra
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user 5998
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
1
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What are non-trivial examples of non-singular blow-ups of a non-singular variety?
For $X=\mathbb{A}^3$ you may take as $Z$ the three coordinate axes defined by $(x,y)(x,z)(y,z)$: The blowup $Bl_Z(X)$ of $X$ in $Z$ is nonsingular. However $Bl_Z(X)$ is isomorphic to a composition of …
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7
votes
When is a blow-up non-singular?
For monomial ideals there is a combinatorial smoothness criterion, see "Blowups in tame monomial ideals" https://arxiv.org/abs/0905.4511
- 205
5
votes
3
answers
409
views
CM for primary ideal
Let $R$ be a regular local ring, $I$ a prime ideal and $J$ an $I$-primary ideal in $R$. Is it true that if $R/I$ is CM then also $R/J$ is CM?
This question is in some way the inverse of this one.
- 205
2
votes
1
answer
1k
views
Irreducible components of reduced complete intersection
Let $Z$ be an irreducible and reduced scheme. Does there exist a reduced complete intersection $Y$ such that $Z$ is an irreducible component of $Y$?
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1
vote
Groebner bases for power series rings (reference request)
There is also a nice treatment of standard bases in the ring of convergent power series in the book of De Jong and Pfister "Local analytic geometry: Basic theory and applications" (it's chapter 7).
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