Initial logarithmic Lie algebras of hypersurface singularities

Details Initial logarithmic Lie algebras of hypersurface singularities Initial logarithmic Lie algebras of hypersurface singularities

2008-07-11

arxiv.org/abs/0807.1916v2

J. Lie Theory 19,2 (2009), 209-221

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We introduce a Lie algebra of initial terms of logarithmic vector fields along a hypersurface singularity. Extending the formal structure theorem in [GS06, Thm. 5.4], we show that the completely reducible part of its linear projection lifts formally to a linear Lie algebra of logarithmic vector fields. For quasihomogeneous singularities, we prove convergence of this linearization. We relate our construction to the work of Hauser and M"uller [M"ul86, HM89] on Levi subgroups of automorphism groups of singularities, which proves convergence even for algebraic singularities. Based on the initial Lie algebra, we introduce a notion of reductive hypersurface singularity and show that any reductive free divisor is linear. As an application, we describe a lower bound for the dimension of hypersurface singularities in terms of the semisimple part of their initial Lie algebra.

Affiliated with

Also associated with

No associations

Rating

Initial logarithmic Lie algebras of hypersurface singularities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Initial logarithmic Lie algebras of hypersurface singularities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Initial logarithmic Lie algebras of hypersurface singularities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-576402