Timeline for Given a subspace $U \subseteq S^d(V)$ of a particular form, does there always exist a complement of the form $S^d(W)$?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2022 at 15:21 | vote | accept | Ben | ||
| Feb 17, 2022 at 21:21 | history | edited | LSpice | CC BY-SA 4.0 |
Inline link to previous question; other mild TeXing
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| Feb 17, 2022 at 19:42 | answer | added | Libli | timeline score: 1 | |
| Feb 15, 2022 at 14:48 | comment | added | Ben | If a subvariety $X \subseteq V$ is s.t. $I(X)$ is generated by degree-d polynomials, then $U_X=\text{span}\{u^{\vee d} : u \in X\}$ is of the specified form, and any linear subspace $W \subseteq V$ for which $U_X \cap S^d(W)=\{0\}$ satisfies the property that $X \cap W=\{0\}$. In general, checking whether $X \cap W=\{0\}$ seems computationally intractable, but now we can do it efficiently when $\dim(W)$ is small enough. I want to know what the maximum possible dimension of $W$ is that this method can handle (the method will then be able to handle a generic $W$ of this dimension). | |
| Feb 15, 2022 at 12:33 | comment | added | Libli | Just to be curious : are there any (geometric or algebraic) motivations behind this question? Does it come from studying Lefschetz type results for Jacobian rings or something related? | |
| Feb 14, 2022 at 19:59 | history | asked | Ben | CC BY-SA 4.0 |