Milnor fiber

Milnor fiber, Milnor map and Milnor fibration

For a hypersurface in $\mathbf{C}^{n+1}$ given by an equation $f = 0$ for some $f\in\mathbf{C}[[z_0,z_1,\ldots,z_n]]$ 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