arXiv Analytics

Sign in

arXiv:0906.2920 [math.AG]AbstractReferencesReviewsResources

On the Milnor fibers of sandwiched singularities

Andras Nemethi, Patrick Popescu-Pampu

Published 2009-06-16Version 1

The sandwiched surface singularities are those rational surface singularities which dominate birationally smooth surface singularities. de Jong and van Straten showed that one can reduce the study of the deformations of a sandwiched surface singularity to the study of deformations of a 1-dimensional object, a so-called decorated plane curve singularity. In particular, the Milnor fibers corresponding to their various smoothing components may be reconstructed up to diffeomorphisms from those deformations of associated decorated curves which have only ordinary singularities. Part of the topology of such a deformation is encoded in the incidence matrix between the irreducible components of the deformed curve and the points which decorate it, well-defined up to permutations of columns. Extending a previous theorem ofours, which treated the case of cyclic quotient singularities, we show that the Milnor fibers which correspond to deformations whose incidence matrices are different up to permutations of columns are not diffeomorphic in a strong sense. This gives a lower bound on the number of Stein fillings of the contact boundary of a sandwiched singularity.

Comments: 16 pages, 5 figures
Journal: International Math. Research Notices, Vol. 2010, No. 6, 1041-1061
Categories: math.AG, math.SG
Subjects: 32S55, 53D10, 32S25, 57R17
Related articles: Most relevant | Search more
arXiv:0805.3449 [math.AG] (Published 2008-05-22, updated 2009-05-06)
On the Milnor fibers of cyclic quotient singularities
arXiv:1310.8050 [math.AG] (Published 2013-10-30, updated 2013-10-31)
Deformation of singularities and additive invariants
arXiv:1409.5053 [math.AG] (Published 2014-09-17)
Fibrations structure and degree formulae for Milnor fibers