On the cohomology of the complement of the bifurcation diagram of the singularity \(A_ \mu\)
Let \(\mathbb{C}^{\mu - 1}\) be the space of polynomials \(f(z) = z^{\mu - 1} + a_ 1 z^{\mu - 1} + \dots + a_{\mu- 1} z\), \(a_ i \in \mathbb{C}\). The space of polynomials of general position in \(\mathbb{C}^{\mu - 1}\) is the complement to a hypersurface \(\Xi\) consisting of two irreducible components. One of them is caustic \(\Sigma\) formed by the polynomials with degenerate critical points \((f'(z) = f''(z) = 0)\). The other -- Maxwell stratum \(M\) -- is the closure of the set of polynomials with coinciding critical values. The set \(\Xi\) is the function bifurcation diagram of the singularity \(A_ \mu\). In the article under review the local cohomology ring of the complement of the bifurcation diagram is studied.
scientific article; zbMATH DE number 687599
scientific article