Automorphisms of P 8 singularities and the complex crystallographic groups

Victor Goryunov; Dmitry Kerner

doi:10.1134/S0081543809040075

Automorphisms of P ₈ singularities and the complex crystallographic groups

Victor Goryunov
, Dmitry Kerner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The paper completes the study of symmetries of parabolic function singularities with relation to complex crystallographic groups that was started by the first co-author and his collaborator. We classify smoothable automorphisms of P₈ singularities which split the kernel of the intersection form on the second homology. For such automorphisms, the monodromy groups acting on the duals to the eigenspaces with degenerate intersection form are then identified as some of complex affine reflection groups tabled by V. L. Popov.

Original language	English
Pages (from-to)	91-103
Number of pages	13
Journal	Proceedings of the Steklov Institute of Mathematics
Volume	267
Issue number	1
DOIs	https://doi.org/10.1134/S0081543809040075
State	Published - 1 Dec 2009

ASJC Scopus subject areas

Mathematics (miscellaneous)

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title = "Automorphisms of P 8 singularities and the complex crystallographic groups",

abstract = "The paper completes the study of symmetries of parabolic function singularities with relation to complex crystallographic groups that was started by the first co-author and his collaborator. We classify smoothable automorphisms of P8 singularities which split the kernel of the intersection form on the second homology. For such automorphisms, the monodromy groups acting on the duals to the eigenspaces with degenerate intersection form are then identified as some of complex affine reflection groups tabled by V. L. Popov.",

author = "Victor Goryunov and Dmitry Kerner",

note = "Funding Information: Both authors gratefully acknowledge the support of the EC Marie Curie Training Site (LIMITS) on Algebraic Geometry, Singularities and Knot Theory, which funded the visits of the second author to Liverpool. The research of the second author was also supported by the Skirball postdoctoral fellowship of the Center of Advanced Studies in Mathematics, Be{\textquoteright}er Sheva, Israel.",

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AU - Kerner, Dmitry

N1 - Funding Information: Both authors gratefully acknowledge the support of the EC Marie Curie Training Site (LIMITS) on Algebraic Geometry, Singularities and Knot Theory, which funded the visits of the second author to Liverpool. The research of the second author was also supported by the Skirball postdoctoral fellowship of the Center of Advanced Studies in Mathematics, Be’er Sheva, Israel.

PY - 2009/12/1

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N2 - The paper completes the study of symmetries of parabolic function singularities with relation to complex crystallographic groups that was started by the first co-author and his collaborator. We classify smoothable automorphisms of P8 singularities which split the kernel of the intersection form on the second homology. For such automorphisms, the monodromy groups acting on the duals to the eigenspaces with degenerate intersection form are then identified as some of complex affine reflection groups tabled by V. L. Popov.

AB - The paper completes the study of symmetries of parabolic function singularities with relation to complex crystallographic groups that was started by the first co-author and his collaborator. We classify smoothable automorphisms of P8 singularities which split the kernel of the intersection form on the second homology. For such automorphisms, the monodromy groups acting on the duals to the eigenspaces with degenerate intersection form are then identified as some of complex affine reflection groups tabled by V. L. Popov.

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Automorphisms of P ₈ singularities and the complex crystallographic groups

Abstract

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