# Tagged Questions

for questions about algebraic geometry that focus on affine space. For affine mappings in linear algebra (i.e. linear mappings plus translations), please use the linear-algebra tag or another appropriate tag.

2answers
109 views

### Finding the defining equations for a simple quotient variety

First of all let me note that I have no experience at all with modern algebraic geometry so if at all possible I would appreciate an answer not involving the concept of a scheme. I have however some ...
1answer
38 views

### Flexible affine variety

Let X be an affine variety. Aut(X) is automorphisms group of X. SAut(X) is a subgroup spanned by all unipotent(image of additive group of field K) subgruops. X is called flexible if SAut(X) act ...
0answers
17 views

### How do projections in 3D with homogeneous coordinates work?

Affine 3D transformations can be expressed in homogeneous coordinates by a matrix $M \in \mathbb{R}^{4 \times 4}$. This means we have 16 parameters to calculate. The first thing I asked myself is how ...
5answers
75 views

### Prove 3 vectors are collinear

I am asked to prove A(2,4), B(8,6), C(11,7) are collinear using vectors. I can work AB by subtracting A from B and BC by subtracting B from C in vector form. I can say that BC = 2AB. But I don't ...
1answer
37 views

1answer
43 views

0answers
33 views

### Complete affine variety is a finite set

When I read Newstead's book, "Introduction to Moduli Problems", I found on page 5 the following sentence: "It is easy to see that if $X$ is a complete irreducible variety, then $A(X)=k$; it follows ...
0answers
86 views

### Affine-regular hexagon in convex body

An affine-regular $n$-gon is a non-degenerate affine image of the regular $n$-gon. It seems to be a standard fact in combinatorial geometry that inside every convex compact set $K\subseteq \mathbb R^2$...
0answers
49 views

### Could we talk about affine spaces before vector spaces?

I was recommended the book Geometry by Michele Audin by a professor when I asked about learning more about affine geometry. I like the book, but it's raised a question. To me, it seems that it would ...