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Results tagged with ac.commutative-algebra
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user 7780
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
1
vote
1
answer
424
views
Flat family: limit of intersection vs intersection of limits
Consider a $\textbf{flat}$ surjective map $f: X \rightarrow \mathbb{A}^1$. The general fibers $F_{\epsilon}$ are canonically isomorphic, and the special fiber $F_0$ above $0 \in \mathbb{A}^1$ is not i …
- 1,719
4
votes
1
answer
821
views
Equi-dimensionality of special fibers in a flat family
Given a flat map $f: X \rightarrow Y$ such that $X$ is a projective variety and $Y$ is a smooth curve. Each generic fiber is isomorphic to an irreducible projective variety $A$ of dimension $d$.
The …
- 1,719