nLab 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

Relation to local systems on the complement of a union of complex hyperplanes (arrangement of hyperplanes)

• Daniel Cohen, A. Suciu, On Milnor fibrations of arrangements, J. London Math. Soc. 51 (1995) 105–119; MR96e:32034 doi

For meromorphic functions (instead of holomorphic)

• Arnaud Bodin, Anne Pichon, José Seade, Milnor fibrations of meromorphic functions, J. London Math. Soc. 51:1 (1995) 105–119 doi

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