@article{5f5453bb3d834c349ce7896ebc8ae8d1,
title = "Enumeration of uni-singular algebraic hypersurfaces",
abstract = "We enumerate complex algebraic hypersurfaces in n, of a given (high) degree with one singular point of a given singularity type. Our approach is to compute the (co)homology classes of the corresponding equisingular strata in the parameter space of hypersurfaces. We suggest an inductive procedure, based on an intersection theory combined with liftings and degenerations. The procedure computes the (co)homology class in question, whenever a given singularity type is properly defined and the stratum possesses good geometric properties. We consider in detail the generalized Newton-non-degenerate singularities. We also give examples of enumeration in some other cases.",
author = "D. Kerner",
note = "Funding Information: This work was initiated during the conference: {\textquoteleft}Singularities and Computer Algebra{\textquoteright} on the occasion of Gert-Martin Greuel{\textquoteright}s 60th birthday (at Universit{\"a}t Kaiserslautern). I would like to thank the organizers for the invitation, L. Bodnarchuk and I. Burban for the hospitality and numerous important conversations. The work was inspired by R. Piene who encouraged me and gave important advice. To perform the explicit numerical calculations, I had to use computer programs. I would like to thank B Noyvert for numerous computational tricks; they tremendously simplified the process. I would like to thank the referees for careful reading of the text; their comments helped to improve it significantly. Special thanks are to G. M. Greuel and A. Nemethi, who saved me from making numerous errors in singularity of hypersurfaces. The research was constantly supported by the Hermann-Minkowski Minerva Center for Geometry at Tel-Aviv University and by Israel Science Foundation grant, no. 465/04.",
year = "2008",
month = jan,
day = "1",
doi = "10.1112/plms/pdm036",
language = "English",
volume = "96",
pages = "623--668",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "John Wiley and Sons Ltd",
number = "3",
}