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Milnor Fiber Boundary of a Non-isolated Surface Singularity

  • András Némethi
  • Ágnes Szilárd

Part of the Lecture Notes in Mathematics book series (LNM, volume 2037)

Table of contents

  1. Front Matter
    Pages i-xii
  2. András Némethi, Ágnes Szilárd
    Pages 1-7
  3. Preliminaries

    1. Front Matter
      Pages 9-9
    2. András Némethi, Ágnes Szilárd
      Pages 11-15
    3. András Némethi, Ágnes Szilárd
      Pages 17-23
    4. András Némethi, Ágnes Szilárd
      Pages 25-43
    5. András Némethi, Ágnes Szilárd
      Pages 45-54
    6. András Némethi, Ágnes Szilárd
      Pages 63-77
    7. András Némethi, Ágnes Szilárd
      Pages 79-82
    8. András Némethi, Ágnes Szilárd
      Pages 83-97
  4. Plumbing Graphs Derived from $$\mathit\Gamma_{\mathcal{C}}$$

    1. Front Matter
      Pages 99-99
    2. András Némethi, Ágnes Szilárd
      Pages 101-115
    3. András Némethi, Ágnes Szilárd
      Pages 117-130
    4. András Némethi, Ágnes Szilárd
      Pages 131-138
    5. András Némethi, Ágnes Szilárd
      Pages 139-151
    6. András Némethi, Ágnes Szilárd
      Pages 153-156
    7. András Némethi, Ágnes Szilárd
      Pages 157-160
    8. András Némethi, Ágnes Szilárd
      Pages 161-166
    9. András Némethi, Ágnes Szilárd
      Pages 167-172
    10. András Némethi, Ágnes Szilárd
      Pages 173-176
  5. Examples

    1. Front Matter
      Pages 177-177
    2. András Némethi, Ágnes Szilárd
      Pages 179-199
    3. András Némethi, Ágnes Szilárd
      Pages 201-204
    4. András Némethi, Ágnes Szilárd
      Pages 205-208
    5. András Némethi, Ágnes Szilárd
      Pages 209-210
    6. András Némethi, Ágnes Szilárd
      Pages 211-214
  6. What Next?

    1. Front Matter
      Pages 215-215
    2. András Némethi, Ágnes Szilárd
      Pages 217-222
  7. Back Matter
    Pages 223-240

About this book

Introduction

In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized

Keywords

32Sxx, 14J17, 14B05, 14P15, 57M27 monodromy non-isolated singularity plumbed 3-manifolds resolution graphs

Authors and affiliations

  • András Némethi
    • 1
  • Ágnes Szilárd
    • 2
  1. 1.Algebraic Geometry and Differential TopoRényi Institute of MathematicsBudapestHungary
  2. 2.Algebraic Geometry and Differential TopoRényi Institute of MathematicsBudapestHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-23647-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-23646-4
  • Online ISBN 978-3-642-23647-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site