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Autumn School: "Topology of Singularities"

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This is an autumn school of the SFB/TRR 45 Bonn-Essen-Mainz financed by Deutsche Forschungsgemeinschaft. It takes place September 19-23, 2011 at the University of Mainz.

  • Summer School
When Sep 19, 2011 09:00 AM to
Sep 23, 2011 02:00 PM
Where Mainz, 05-426 (Lectures), 05-432 (Registration)
Contact Name
Contact Phone +49-6131-3922327
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The school aims to introduce the audience to the topology of singularities over the field of complex numbers. We will start with the basic theory and intend to reach active fields of research by the end of the week. The emphasis will be on practical aspects. The lectures address PhD students and Postdocs in the field of algebraic or complex geometry with a basic knowledge in classical topology.


  • Michael Bogner (Mainz)
  • Christian Lehn (Mainz)
  • Duco van Straten (Mainz)



  • Norbert A'Campo (Basel): Topology of complex hypersurface singularities.
  • Michael Lönne (Bayreuth): Topology of plane curves, local and global.
    Topics of the lecture course will be: topology of plane curve singularities, its link, the braid, the concept of monodromy, basics of the braid group, Puiseux theorem, braid monodromy.
  • András Némethi (Budapest): Some invariants of normal surface singularities
  • Jonathan Wahl (Chapel Hill, North Carolina, USA): Q-Gorenstein smoothings of normal surface singularities.




Time Monday Tuesday Wednesday Thursday Friday
9:00 registration  
9:30-10:30 A'Campo

Lönne A'Campo/Lönne exc. Némethi/
Wahl (2)
10:30-11:00 coffee break
11:00-12:00 Lönne
A'Campo Wahl* Lönne
12:15-13:15 Wahl*
A'Campo Wahl*
Némethi Némethi
13:15-14:00 lunch
preparation for exercises
15:00-17:00 preparation for exercises

coffee break
Guided Tour:
coffee break

exc. A'Campo/
Lönne (1)
exc. Némethi/
Wahl (1)
Town of Mainz
exc. A'Campo/
Lönne (2)


sparkling wine tasting

 exc.= exercise session

 * It is recommended that you read the first 6-7 pages of Wahl, Jonathan "Topology, geometry, and equations of normal surface singularities," in Singularities and Computer Algebra, LMS Lecture Note Series (No. 324), Cambridge University Press (2006), as preparation.

References for preparation:



  • Brieskorn, Egbert; Knörrer, Horst Plane: Algebraic Curves. Translated from the German by John Stillwell. Birkhäuser Verlag, Basel, 1986. vi+721 pp. ISBN: 3-7643-1769-8,
  • Ebeling, Wolfgang: The monodromy groups of isolated singularities of complete  intersections. Lecture Notes in Mathematics, 1293. Springer-Verlag, Berlin, 1987. xiv+153 pp. ISBN: 3-540-18686-7
  • Fischer, Gerd: Plane algebraic curves. Student Mathematical Library, 15. American Mathematical Society, Providence, RI, 2001. xvi+229 pp. ISBN: 0-8218-2122-9


  • Five lectures on normal surface singularities; lectures delivered at the Summer School in "Low dimensional topology'', Budapest, Hungary 1998; Proceedings of the Summer School, Bolyai Society Mathematical Studies 8, Low Dimensional Topology, 269-351 (1999).
  • Some topological invariants of isolated hypersurface singularities, Five lectures of the EMS-Summer School, Eger (Hungary) 1996, Proceedings of the Summer School, Bolyai Society Mathematical Studies 8, Low Dimensional Topology,   353-413 (1999).
  • Invariants of normal surface singularities, Proceedings of the Conference: Real and Complex Singularities, San Carlos, Brazil, August 2002; Contemporary Mathematics354, 2004, 161-208.
  • Graded roots and singularities,  Proceedings Advance School and Workshop on Singularities in Geometry and Topology ICTP (Trieste, Italy), World Sci. Publ., Hackensack, NJ, 2007, 394-463.
  • Lattice cohomology of normal surface singularities, Publ. RIMS. Kyoto Univ., 44 (2008), 507-543.
  • Poincaré series associated with surface singularities, Singularities I: Algebraic and Analytic Aspects, International Conference in Honor of the 60th Birthday of Lê Dung Tráng, 2007,  Cuernavaca, Mexico,  Contemporary Mathematics, 474, 2008, 271-299.
  • "Chapters on Algebraic Surfaces" by Miles Reid



  • Milnor, John: Singular points of complex hypersurfaces", Ann. of Math. Studies 91 (1968).
  • Mumford, David: "The topology of normal singularities of an algebraic surface and a criterion for simplicity," Publ. Math. IHES 9 (1962)
  • Hirzebruch: Bourbaki talk on that paper (Seminaire Bourbaki, 1962/63, No. 250).
  • Pinkham, Henry: "Deformations of normal singularities with C*-action,"
    Math. Ann. 232 (1978), 65-84.
  • Wahl, Jonathan: "On rational homology disk smoothings of valency 4 surface singularities".
  • Wahl, Jonathan: "Topology, geometry, and equations of normal surface singularities," in Singularities and Computer Algebra, LMS Lecture Note Series (No. 324), Cambridge University Press (2006).


Applications and Financial Support

Full financial support is available for members of the SFB/TRR 45. There is limited support for other participants, too. Please register by filling out the registration form; deadline for application is August 31, 2011.

We kindly as applicants who register later than August 19, 2011 to take care of hotel reservation themselves. For that, we refer to the survey page of the city of Mainz where you can find a detailed list of hotels in and around Mainz.


Travel information

All lectures will take place in the Mathematics Department of the University of Mainz, Staudinger Weg 9, in room 05-426. Here is a map of the campus. The closest airport is located at Frankfurt/Main. Find your way from the airport to the institute here.




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