μ -constant monodromy groups and marked singularities

Claus Hertling[1]

  • [1] Universität Mannheim Lehrstuhl für Mathematik VI Seminargebäude A 5, 6 68131 Mannheim (Germany)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 7, page 2643-2680
  • ISSN: 0373-0956

Abstract

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μ -constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a fixed singularity is studied. It consists of automorphisms of the Milnor lattice which respect not only the intersection form, but also the Seifert form and the monodromy. We conjecture that it contains all such automorphisms, modulo ± id . Second, marked singularities are defined and global moduli spaces for right equivalence classes of them are established. The conjecture on the group would imply that these moduli spaces are connected. The relation with Torelli type problems is discussed and a new global Torelli type conjecture for marked singularities is formulated. All conjectures are proved for the simple and 22 of the 28 exceptional singularities.

How to cite

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Hertling, Claus. "$\mu $-constant monodromy groups and marked singularities." Annales de l’institut Fourier 61.7 (2011): 2643-2680. <http://eudml.org/doc/275459>.

@article{Hertling2011,
abstract = {$\mu $-constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a fixed singularity is studied. It consists of automorphisms of the Milnor lattice which respect not only the intersection form, but also the Seifert form and the monodromy. We conjecture that it contains all such automorphisms, modulo $\pm \operatorname\{id\}$. Second, marked singularities are defined and global moduli spaces for right equivalence classes of them are established. The conjecture on the group would imply that these moduli spaces are connected. The relation with Torelli type problems is discussed and a new global Torelli type conjecture for marked singularities is formulated. All conjectures are proved for the simple and $22$ of the $28$ exceptional singularities.},
affiliation = {Universität Mannheim Lehrstuhl für Mathematik VI Seminargebäude A 5, 6 68131 Mannheim (Germany)},
author = {Hertling, Claus},
journal = {Annales de l’institut Fourier},
keywords = {$\mu $-constant deformation; monodromy group; marked singularity; moduli space; Torelli type problem; symmetries of singularities; -constant deformatiom},
language = {eng},
number = {7},
pages = {2643-2680},
publisher = {Association des Annales de l’institut Fourier},
title = {$\mu $-constant monodromy groups and marked singularities},
url = {http://eudml.org/doc/275459},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Hertling, Claus
TI - $\mu $-constant monodromy groups and marked singularities
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 7
SP - 2643
EP - 2680
AB - $\mu $-constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a fixed singularity is studied. It consists of automorphisms of the Milnor lattice which respect not only the intersection form, but also the Seifert form and the monodromy. We conjecture that it contains all such automorphisms, modulo $\pm \operatorname{id}$. Second, marked singularities are defined and global moduli spaces for right equivalence classes of them are established. The conjecture on the group would imply that these moduli spaces are connected. The relation with Torelli type problems is discussed and a new global Torelli type conjecture for marked singularities is formulated. All conjectures are proved for the simple and $22$ of the $28$ exceptional singularities.
LA - eng
KW - $\mu $-constant deformation; monodromy group; marked singularity; moduli space; Torelli type problem; symmetries of singularities; -constant deformatiom
UR - http://eudml.org/doc/275459
ER -

References

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