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Results tagged with polynomials
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user 43593
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
3
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answer
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Polynomials with Unique Critical Value
My question is extremely simple to state: I am looking for a characterization of multivariate complex polynomials $f$ such that $f(Sing(f))=\{0\}$. … If that question ends up being easy, is there a good characterization known of multivariate polynomials over an arbitrary algebraically closed field only possessing one critical value? …
- 141
1
vote
Accepted
Polynomials with Unique Critical Value
Whoops, figured it out, at least in the case of complex polynomials.
We're looking for the set of $f$ such that $Z(f)=f^{-1}(0)\subseteq Z(j(f))$, where $j(f)$ denotes the Jacobian ideal of $f$. …
- 141