I'm learning about intersection cohomology topologically through MacPherson's "New York Times Article". This is a very nice guide which gives a nice idea on how to use these methods for low-dimensional topological spaces, I'm not sure how I can compute the intersection homology for higher dimensional varieties. For example, if I take the quintic threefold $$ \textbf{Proj}\left( \frac{\mathbb{C}[x,y,z,w,u]}{(x^5 + y^5 + z^2wu^2 + x^3y^2)} \right) $$ It has jacobian $$ \text{Jac}(f) = [5x^4 + 3x^2y^2, 5y^4 + 2x^3y, 2zwu^2, z^2u^2, 2z^2wu] $$ hence ther are the singular loci along the rational curves $$ x,y,z = 0, \text{ } x,y,u=0 $$ We can form a normal stratification on this variety with these stratum, but now I'm not sure how to actually compute the intersection cohomology groups from here.

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Singular Intersection Homologyis at faculty.tcu.edu/gfriedman/IHbook.pdf $\endgroup$ – Steve Huntsman Jul 21 '16 at 20:53