nLab
Milnor fiber

Milnor fiber, Milnor map and Milnor fibration

For a hypersurface in C n+1\mathbf{C}^{n+1} given by an equation f=0f = 0 for some fC[[z 0,z 1,,z n]]f\in\mathbf{C}[[z_0,z_1,\ldots,z_n]] with an isolated singularity at zero…

  • John Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies 61, Princeton Univ. Press 1968 iii+122 pp. MR239612
  • P. Seidel, Fukaya categories and Picard-Lefschetz theory, Zurich Lectures in Advanced Mathematics. European Mathematical Society, Zürich, 2008. viii+326 pp. MR2009f:53143, doi
  • Sec. I.1 in V. Kulikov, Mixed Hodge structures and singularities, Cambridge Univ. Press 1998, xxii+186 pp.
  • Nero Budur, Singularity invariants related to Milnor fibers: survey, arxiv/1012.3150

There is also a rigid analytic version analytic Milnor fiber, which is a rigid variety over the nonarchimedean field of complex Laurent series associated to a complex hypersurface singularity. It has been used in the study of motivic zeta function via motivic integration on rigid varieties in

  • J. Nicaise, J. Sebag, Motivic Serre invariants, ramification, and the analytic Milnor fiber, Invent. Math. 168:1, 133–173 (2007) MR0239612

Last revised on January 19, 2021 at 18:53:18. See the history of this page for a list of all contributions to it.