1. ### A The map from a complex torus to the projective algebraic curve

I am following the proof to show that the complex torus is the same as the projective algebraic curve. First we consider the complex torus minus a point, punctured torus, and show there is a biholomorphic map or holomorphic isomorphism with the affine algebraic curve in ##\mathbb{C}^2##...
2. ### Projective Plane Proof

Homework Statement Let P(W) be a projective space whose dimension is greater than or equal to 2 and let three non-colinear projective points, [v_{1}],[v_{2}],[v_{3}]\in P(W) . Prove that there is a projective plane in P(W) containing all three points. Homework Equations The Attempt at a...
3. ### A Concept of duality for projective spaces and manifolds

I firstly learned about duality in context of differentiable manifolds. Here, we have tangent vectors populating the tangent space and differential forms in its co-tangent counterpart. Acting upon each other a vector and a form produce a scalar (contraction operation). Later, I run into the...
4. ### A Why are conics indistinguishable in projective geometry?

It is said that curves of the second order which we usually refer to as ellipse, parabola and hyperbola, i. e. conics, are all represented on projective plane by closed curves (oval curve), which means there is no distinction between them. Why is it? Projective space can, in principle, be...
5. ### 2D Projective Complex Space, Spin

Just reviewing some QM again and I think I'm forgetting something basic. Just consider a qubit with basis {0, 1}. On the one hand I thought 0 and -0 are NOT the same state as demonstrated in interference experiments, but on the other hand the literature seems to say the state space is...