Topology of complex polynomials via polar curves
The authors consider the global polar curves associated with an affine smooth hypersurface \(F\) in \(\mathbb{C}^n\). If \(f\in \mathbb{C}[x_1, \dots,x_n]\) is a polynomial such that the fiber \(F_t:= f^{-1}(t)\) is smooth and connected, the main result computes the Euler characteristic \(\chi(F_t)\) of \(F_t\) in terms of the polar invariants of the intersections \(F_t\cap E^k\), where \(E^k\) is a general linear subspace of \(\mathbb{C}^n\) of codimension \(k\), \(k=0,1, \dots,n-1\).
scientific article; zbMATH DE number 1333304
scientific article