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Results tagged with polynomials
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user 124862
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.
6
votes
Accepted
Singular locus of the discriminant variety
(Details of what follows can be found in any exposition of dual varieties such as Lamotke's paper.)
Given a smooth projective variety $X\subset\mathbb{P}^M$ we can look at the subvariety $D(X)\subset\ …
- 1,566
1
vote
Can one deduce the fundamental theorem of algebra from real calculus and linear algebra?
(Expansion of my comment above.) This does not answer the diagonalisability of all matrices. It just extends it from symmetric to normal.
Assume that we have an ordered field $R$ for which one can pro …
- 1,566
2
votes
Accepted
Dimension of the set of singular hypersurfaces
Given a smooth projective variety $X\subset\mathbb{P}^{N-1}$, let $I(X)\subset X\times(\mathbb{P}^{N-1})^*$ denote the locus of pairs $(x,H)$ where $x\in H$ and $T_x(X)\subset T_x(H)$; here we are thi …
- 1,566