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Results tagged with reference-request
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user 1508
This tag is used if a reference is needed in a paper or textbook on a specific result.
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Terminology for the image of the diagonal embedding.
Let $X$ be a topological space equipped with maps into two spaces $\bar X_1$ and $\bar X_2$. Is there a standard notation/terminology for the closure $\bar X$ in $\bar X_1 \times \bar X_2$ of the dia …
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References for literature from mathematicians who provided critiques and proposals concernin...
Jonathan Korman (a mathematician) and Wing-Yee Tong (an artist) coauthored The NSA and the Social Responsibility of Mathematicians in the December 2016 issue of The Mathematical Intelligencer. It argu …
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Algebraic curve cannot suddenly end
Following the idea of Felipe Voloch, I try to give a simple proof based on Puiseux series expansion. Let $C$ be a real algebraic curve at the origin. Look at the Puiseux series expansion (say in terms …
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Is a toric variety over a field of positive characteristic complete if and only if the suppo...
The answer is yes. Fulton's proof is in fact valid positive characteristic as well. In the proof of "full support $\Rightarrow$ completeness" he uses the valuative criterion which, as you noticed, is …
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When $k(f(x), g(x)) = k(x)$? In other words, when is a given polynomial parametrization of a...
If $f, g \in k[x]$, where $k$ is a field, then $k(f, g) = k(h)$ for some rational function $h \in k(x)$ (this is a special case of Lüroth's theorem).
Question 1: Under what conditions does the above h …
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Discovery of Hilbert polynomial
Presumably it was Hilbert who discovered Hilbert polynomials - where did they first appear?
The basic theorem is that for a finitely generated graded module $M = \bigoplus_k M_k$ over the ring of poly …
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