The Topology of Complex Hypersurfaces
نویسنده
چکیده
Let f be a polynomial in n+1 complex variables. In this paper, we study the topology of the set V = f−1(0). While V is a differentiable manifold in the neighborhood of simple points, the topology is more complicated at singular points. We use the following construction to study the topology at singular points. Let S be a small sphere around a singular point, and let K = S ∩V . We will prove that S −K is a smooth fiber bundle over S1, with fibers homotopy equivalent to a CW complex of dimension ≤ n, which allows us to obtain substantial information about the fibers. Finally, we show that K is a (n− 2)-connected differentiable manifold.
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