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Abstract:
The regular, Zk-covers
of a finite CW-complex X are parametrized by the points in the Grassmannian of k-planes in H1(X,Q).
Moving about this rational Grassmannian, and recording
when the sum of the Betti numbers (up to degree i)
of the corresponding covers is finite carves out certain
subsets Ωik(X) of Grk (H1(X,Q)).
I will present a method (which in rough outline goes back to Dwyer and Fried) for determining these sets, using the incidence correspondence between projective varieties and subvarieties of the Grassmannian.
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