# Questions tagged [intersection-theory]

In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring. (Ref: http://en.m.wikipedia.org/wiki/Intersection_theory). Do not use this tag for elementary problems in linear algebra or geometry. (e.g. determining whether two lines intersect)

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### Intersection of superellipse with line

My goal is to do a stereographic-like projection of the plane but on a $L_p$ sphere and with the projection between the pole and the center of the sphere. For that I begin with 2D stereographic-like ...
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### Finding intersection between straight line and spherical line

I'm trying to find the intersection between two functions. The first function describes the red straight line in the figure: $$\tan\epsilon_1=\frac{d(z)-d_{01}}{z-z_{01}}$$ The second function ...
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### Understanding why set theoretic intersection is not necceraly a complete intersection

If it is true that for projective varieties one can show that: $Z(f_1, f_2) = Z(f_1)\cap Z(f_2)$ for any homogenous polynomials, than why isn't true than any set theoretic complete intersection of ...
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### Inverse direction of Hodge index theorem

The Hodge index theorem states that the intersection matrix associated to curves on a smooth algebraic surface has a specified signature---namely, if the intersection matrix has size $n \times n$ then ...
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### What is the probability of three union if one of the events has probability zero?

my problem is this: We throw $n$ bells randomly into $3$ boxes initially empty. Compute the probability that at least One boxes remaining empty. I have the solution and that is:  P(A_1 \cup A_2 \cup ...
Let's consider a closed and oriented 4-manifold $M_4$ and denote $H_2(M_4,\mathbb{Z})$ as the homology group of 2-cycles and $Q_{M_4}(S_{A},S_{B})$ as the symmetric intersection pairing between 2-...