The Milnor fiber of the singularity \(f(x,y) + zg(x,y) = 0\)

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• 作者：Baldur Sigurðsson
• 关键词：Nonisolated hypersurface singularities ; Milnor fiber ; Monodromy zeta function ; Primary 32S05 ; 32S25 ; 32S55 ; 58K10 ; Secondary 14Bxx ; 32Sxx
• 刊名：Revista Matem¨¢tica Complutense
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：29
• 期：1
• 页码：225-239
• 全文大小：463 KB
• 参考文献：1.A’Campo, N.: La fonction zeta d’une monodromie. Comment. Math. Helv. 50, 233–248 (1975)MATH MathSciNet CrossRef
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  3.Eisenbud, D., Neumann, W.: Three-dimensional Link Theory and Invariants of Plane Curve Singularities. Ann. of Math. Stud. Princeton University Press, New Jersey (1985)
  4.Fernández de Bobadilla, J., Menegon Neto, A.: The boundary of the Milnor fibre of complex and real analytic non-isolated singularities. Geom. Dedicata 173, 143–162 (2014)MATH MathSciNet CrossRef
  5.Gompf, R.E., Stipsicz, A.I.: 4-manifolds and Kirby Calculus. Grad. Stud. Math. Amer. Math. Soc. (1999)
  6.Kato, M., Matsumoto, Y.: On the connectivity of the milnor fiber of a holomorphic function at a critical point. In: Manifolds Tokyo 1973, pp. 131–136. Univ. Tokyo Press (1975)
  7.Looijenga, E.J.N.: Isolated Singular Points on Complete Intersections. London Math. Soc. Lecture Note Ser. Cambridge University Press, Cambridge (1984)
  8.Milnor, J.: Singular Points of Complex Hypersurfaces. Ann. of Math. Stud. Princeton University Press, New Jersey (1968)
  9.Némethi, A., Szilárd, Á.: Milnor Fiber Boundary of a Non-isolated Surface Singularity. Lecture Notes in Math. Springer, Berlin (2012)
  10.Wall, C.T.C.: Singular Points of Plane Curves. London Math. Soc. Stud. Text. Cambridge University Press, Cambridge (2004)
  
• 作者单位：Baldur Sigurðsson (1) (2)
  
  1. Alfréd Rényi Institute of Mathematics, 13-15 Reáltánoda u., 1053, Budapest, Hungary
  2. Department of Mathematics, Central European University, Zrínyi u. 14, 1051, Budapest, Hungary
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  Applications of Mathematics
  Geometry
  Mathematics
  Topology
  
• 出版者：Springer Milan
• ISSN：1988-2807

文摘

We give a description of the Milnor fiber and the monodromy of a singularity of the form \(f+zg = 0\), where f and g define germs of plane curve singularities and have no common components. In particular, this gives a description of the boundary of the Milnor fiber. The description depends only on the topological type of the two plane curve germs defined by f and g. As a corollary, we give a simple formula for the monodromy zeta function and the Euler characteristic of the fiber in terms of an embedded resolution of f and g. Keywords Nonisolated hypersurface singularities Milnor fiber Monodromy zeta function