Projective geometry is closely related to perspective geometry. These types of geometry originated with artists around the 14th century.
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How can I compute the multiplicities of the projection map over a smooth projective plane curve?
Suppose that $F$ is a non-singular homogeneous polynomial in $\mathbb{C}^3$ and let $X$ be its zero locus, which is well-defined in $\mathbb{P}^2$. Consider the function $\pi:X\rightarrow\mathbb{P}^1$ ...
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Intersection of smooth projective plane curves
I need to calculate the number of intersections of the smooth projective plane curves defined by the zero locus of the homogeneous polynomials
$$
F(x,y,z)=xy^3+yz^3+zx^3\text{ (its zero locus is ...
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55 views
The genus of the Fermat curve $x^d+y^d+z^d=0$
I need to calculate the genus of the Fermat Curve, and I'd like to be reviewed on what I have done so far; I'm not secure of my argumentation.
Such curve is defined as the zero locus
...
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29 views
How can I define a chart in a smooth projective plane curve?
Consider $F(x,y,z)$ a non-singular homogeneous polynomial of degree $d$. If I consider the zero locus $X=\{[x:y:z]\in\mathbb{P}^2:F(x,y,z)=0\}$
How can I define a complex structure in $X$ in order ...
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32 views
to get a MDS code from a hyperoval in a projective plane
explain how we can get a MDS code of length q+2 and dimension q-1 from a hyperoval
in a projective plane PG2(q) with q a power of 2?
HINT:a hyperoval Q is a set of q+2 points such that no three ...
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91 views
Existence of a special set of q+2 points in the finite affine plane over $\mathbb F_q$
I am working in the finite affine plane over $\mathbb F_q$ with $q=2^n$.
Such a plane has $q^2$ points, $q^2+q$ lines, each line has $q$ points, and by a point is passing $q+1$ lines.
There are $q+1$ ...
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1answer
32 views
An interesting question in planar geometry
Several points in space are projected orthogonally on some three planes alpha, beta, and gamma. Could it happen that in the three projections, plane alpha contains 3 points, plane beta contains 7 ...
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58 views
Number of lines passing through a fixed point in a quadric surface
Suppose that $S \subset \mathbb{P}^3$ is a smooth quadric surface. Let $p \in S$. Can more than two lines $l \subset S$ pass through $p$? If not, why?
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1answer
33 views
Reference request: Projective space $\mathbb{RP}^3$
I have to write seminar paper in Projective geometry and the name of the seminar is (I would try to translate):
Representation of the lines in the projective space $\mathbb{RP}^3-$Kernel, Lineal, ...
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17 views
formula for inverse multidimensional stereographic projection
i'm in need of formula for inverse multidimensional stereographic projection with variant radius of the sphere. Sadly the only ones i'm able to find have either fixed number of dimensions or don't ...
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2answers
126 views
How should I think of lines and planes in projective space?
I have been learning about projective varieties recently and I realised that I have some trouble trying to grasp what lines and planes are even in say $\Bbb{P}^3$. For one, how should I think about a ...
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49 views
Prerequisite for the geometry part of Fulton & Harris book “representation theory”
all,
I am reading Fulton&Harris book and getting stuck in the geometric interpretation of $sl_2\mathbb{C}$. I am not familiar with projective geometry or algebraic geometry and I find that ...
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1answer
35 views
A linear subspace of projective space
If we have a linear subspace of projective $P^n_k$ where $k=\bar k$ that contains all the points $[0:\ldots:0:x:0:\ldots:0]$ with the nonzero $x$ in the $i$th slot for all $i$, how can we see that ...
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1answer
102 views
Learning projective geometry
My ultimate goal is to learn some algebraic geometry with the more concrete immediate goal of understanding things like how $\mathbb R\mathrm P^2$ is embedded in $\mathbb C\mathrm P^2$ or how $\mathbb ...
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1answer
36 views
Projecting two vectors to have constant element-wise euclidean distances
Let $x = (x_{0}, \ldots, x_{n})$ and $y = (y_{0}, \ldots, y_{n})$ be two vectors, and $d = (d_{0} = x_{0} - y_{0}, \ldots, d_{n} = x_{n} - y_{n})$ their element-wise euclidean distances.
My question ...
