A topological interpretation of the Jacobian degree of an arbitrary homogeneous polynomial is given. This leads to classification results for polynomials whose gradients define birational automorphisms of projective space. When the polynomial splits completely into linear factors, the projective space is endowed with a natural Whitney stratification. Transversality conditions for projective subspaces, with respect to the stratification are related to homotopy skeleta of complements of the associated hyperplane arrangement slices. This has implications in twisted homology, in particular Milnor fiber homology and higher homotopy groups.

Keywords:

Arrangements of hyperplanes; Cremona Transformations; Morse theory; homology of local system; Milnor fiber; homotopy groups.

Lecture #10655

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