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Results tagged with ac.commutative-algebra
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user 39777
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
2
votes
Flat algebra over polynomial ring
Let's call $A = k[x_1, \dots, x_r; u_1, \dots, u_s]$. If $u_1, \dots, u_s \in R^\times$, then $i: A \to R$ factors through the localization $A_u$ with respect to $u = u_1 \cdots u_s$. Localization is …
- 505
5
votes
2
answers
767
views
Does the degree of a finite dominant morphism bound the induced degree on subschemes?
Suppose $f: \widetilde{X} \to X$ is a finite dominant morphism between connected, normal, Noetherian schemes, and that this morphism induces a dominant morphism $f_W: \widetilde{W} \to W$ between conn …
- 505
5
votes
Accepted
Geometric interpretation of algebraic tangent cone
You may wish to read the discussion on pages 106-108 of Eisenbud/Harris "The Geometry of Schemes", where they explicitly compute the tangent cone of $(y^2-x^3)$ as a degeneration of the tangent cones …
- 505
2
votes
Accepted
characterisation of regular morphisms
Yes, these are equivalent. See Srikanth Iyengar's write-up on Andr\'e-Quillen homology. Specifically, Theorem 9.5 (together with Proposition 5.9) proves exactly what you want, and a little more. The t …
- 505