Questions tagged [algebraic-geometry]
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The Picard Group: Origin and History
I've come to the notion of the Picard Group.
I was recently linked to this paper paper, which contains the line:
The problem of computing the Picard groups of surfaces $S \subset \mathbb{P}_{\mathbb{...
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0answers
102 views
Did the ancients construct higher genus curves?
I know that the ancients had several ways to construct geometric shapes. I know two of them: the biggest one, ruler and compass, with which you can build some polygons, bisect an angle, etc, but not ...
3
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1answer
93 views
Why is the term "isotropic" used to describe a quadratic form and a vector?
A quadratic form $q$ on a vector space $V$ is isotropic if $q(v) = 0$ admits a nonzero solution. What was this terminology originally intended to evoke?
There is some prior discussion on Math SE, ...
2
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0answers
70 views
Continuation on Galois’ lost memoir(s): was Poisson right in his review of Galois’ memoir?
A recent question asked whether Galois’ “lost” memoir has been since recovered (similar to Abel’s lost memoir). The memoir referenced in the question is the one Galois submitted to the French “...
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1answer
66 views
Who first started parameterizing hyperbolas with hyperbolic functions?
Anyone know the history of using hyperbolic functions to parameterize the parabola? Wolfram hasn't really helped. Anyone know where to look?
3
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1answer
173 views
Origins of Zariski topology
Why did Zariski feel the need to define his famous topology? Was this notion used in one form or another prior to him in algebraic geometry?
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0answers
203 views
First use of term "Hilbert's Nullstellensatz"
This year (2021) marks the 100th anniversary of Emmy Noether's 1921 paper in which she introduced Noetherian rings and proved the primary ideal decomposition for them. The original version of her ...
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0answers
39 views
Who was the first person to prove the invariance of the Euler characteristic under triangulations?
Given a compact orientable surface $S$ and any triangulation where $F$ denotes the amount of triangles, $E$ denotes the amount of edges, and $V$ denotes the amount of vertices, we know that the Euler-...
3
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1answer
109 views
Complete list of publications of Rebecca Barlow
Rebecca Barlow is the discoverer of an interesting surface in algebraic geometry. Is anybody aware of a full list of her contributions? Has she continued working in mathematics in the 21st century?
9
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1answer
372 views
What is the etymology of the mathematical terms "sheaf, stalk, germ"?
The peculiar agricultural terminology commonly used in algebraic geometry and category theory, "sheaf", "stalk", "germ", is quite well-known. A sheaf is pictured as something like a bundle of stalks, ...
6
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1answer
535 views
What was the motive for inventing Gröbner bases?
How did professor Buchberger discover Gröbner (Groebner) bases for polynomial ideals? What was the problem(s) that lead to such a discovery?
5
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2answers
311 views
Who first described the fundamental group as the group of deck transformations?
Grothendieck developed the theory of the fundamental group of a scheme in SGA 1. In order to do so he used the fact that the fundamental group of a topological space is isomorphic to the group of deck ...
8
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2answers
297 views
(Co)Homology: From topology to the rest of mathematics?
I can appreciate how (co)homology arose in the context of topology/geometry. Trying to get a handle on the handles of spaces leads one to this idea. It's not obvious, but I can see how this would lead ...
2
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1answer
126 views
Material models of Riemann surfaces
It is known that during the last quarter of the 19th century there was a flourishing of the production of material models (from plaster, strings, card-board etc) of curves and surfaces in Germany (but ...
2
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3answers
215 views
Who first had the idea to study surfaces via rings of functions, as in algebraic geometry?
This idea provides the foundations of algebraic geometry now; and they have certainly gone down the rabbit hole with it. As a student studying this subject, I have always found it such a great leap to ...
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4answers
2k views
Why are étale morphisms called "étale"?
Alexander Grothendieck developed the theory of "locally trivial coverings spaces for rings/schemes" in SGAI as an analog to the theory of covering spaces in algebraic topology. He called such ...
3
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2answers
198 views
When did mathematician start to draw figures from equation?
I know that when solving geometric problem, Descartes used variables $x,y$ and derived equation such as $y^2=cy-\frac{cxy}{b}+ay-ac$. Conversely, in algebraic geometry, an arbitrary polynomial $F(X_1,....
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2answers
954 views
Where was the word "pencil" first used in (projective) geometry and what is the reason behind this curious name?
The title is pretty self-explanatory: A pencil in projective (or algebraic) geometry is the family of all lines through a point. The above-linked website tells me that Cremona, on page x of Elements ...
13
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2answers
788 views
How did Grothendieck encounter and adopt the categorical language?
Apparently the first mathematical publication of Grothendieck where he uses the terms “functor” and “category” in the technical sense is the Kansas report.
From where Grothendieck had knowledge of ...
5
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1answer
158 views
Origins and history of branched covering
During my research on branched coverings of the projective plane, I am interested to know the origins and history of branched coverings of the projective plane and the projective line, together with ...
6
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1answer
295 views
Grothendieck and elementary topos
I would like to know some references (if any) for the claim that Grothendieck didn't like the idea of elementary topos.
7
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1answer
863 views
Visualizing algebra before Descartes
The Cartesian coordinate system is what I have been told provided the first link between algebra and geometry. However, I also have learned that, for instance, Omar Khayyam solved cubic equations as ...
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3answers
3k views
Grothendieck's approach to solving problems
Alexander Grothendieck is known to have revolutionized several areas of mathematics. His insights were very deep, original and revolutionary. Time after time he showed that he could see in ways that ...
13
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1answer
676 views
Who first introduced the notation $\mathcal{O}$ in algebraic geometry or algebraic number theory
This is my first question for HSM. If it is consider too specialized for HSM, perhaps it can be migrated to MathOverflow.
In algebraic number theory, one frequently denotes the ring of algebraic ...
5
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0answers
194 views
History of Algebraic Geometry for a general readership?
I'm looking for a "pop maths" book on the subject. Something much more accessible than Dieudonné: "light reading" with emphasis on the history, personalities and general ideas and minimal ...
9
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3answers
2k views
What is the history behind the concept of "schemes" in algebraic geometry?
Let me start by saying that I've just started studying algebraic geometry. I have a habit of trying to find out something about the motivation behind new concepts that I'm studying, in this case that ...
16
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1answer
299 views
Did Dedekind show any evidence of pictorial geometric sense?
The most pictorial geometric thinking I find in Dedekind is the intuitive-geometric idea of a continuum which he criticizes as too vague before he gives his account of the continuum based on cuts.
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37
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1answer
7k views
Why did algebraic geometry need Alexander Grothendieck?
Grothendieck is arguably the most brilliant mathematician of the 20th century, with his influence felt the most in algebraic geometry, which he transformed. Some time ago the story used to be told was ...
