Workshop on "Combinatorial and geometric aspects of Hyperplane Arrangements" May 24th through 26th

MAY WORKSHOP: Free abelian covers and arrangements of Schubert varieties

speaker: Alexandru Suciu (Northeastern University)

abstract: The connected, regular, ℤ^k-covers of a finite CW-complex X are parametrized by the points in the Grassmannian of k-planes in V=H¹(X,ℚ). Moving about this rational Grassmannian, and recording when the Betti numbers (up to some fixed degree i) of the corresponding covers are finite carves out certain subsets Ω_kⁱ(X) of Gr_k(V).

In this talk, I will present a method for determining these sets, using the cohomology jumping loci of X, and the incidence correspondence between projective varieties and subvarieties of the Grassmannian. Under favorable conditions, the Ω-invariants are controlled by certain arrangements of special Schubert varieties, which can be computed directly from the cohomology ring of X.

timetable:
Tue 25 May, 14:45 - 15:45, Aula Dini
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