Cohomological connectivity of perturbations of map-germs. (English) Zbl 07849100
Summary: Let \(f: (\mathbb{C}^n, S) \to (\mathbb{C}^p, 0)\) be a finite map-germ with \(n<p\) and \(Y_\delta\) the image of a small perturbation \(f_\delta\). We show that the reduced cohomology of \(Y_\delta\) is concentrated in a range of degrees determined by the dimension of the instability locus of \(f\). In the case \(n \geq p\), we obtain an analogous result, replacing finiteness by \(\mathcal{K}\)-finiteness and \(Y_\delta\) by the discriminant \(\Delta (f_\delta)\). We also study the monodromy associated to the perturbation \(f_\delta\).
© 2023 The Authors. Mathematische Nachrichten published by Wiley-VCH GmbH
© 2023 The Authors. Mathematische Nachrichten published by Wiley-VCH GmbH
MSC:
| 14-XX | Algebraic geometry |
| 14B05 | Singularities in algebraic geometry |
| 32S55 | Milnor fibration; relations with knot theory |
Keywords:
algebraic geometry; derived categories; perverse sheaves; singularity theory; vanishing cyclesReferences:
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