Families of higher dimensional germs with bijective Nash map

Details Families of higher dimensional germs with bijective Nash map Families of higher dimensional germs with bijective Nash map

2006-05-22

arxiv.org/abs/math/0605566v1

Kodai Math. Journal. 31 (2) (2008), 199-218.

Mathematics

Algebraic Geometry

19 pages, 2 figures

Scientific paper

Let (X,0) be a germ of complex analytic normal variety, non-singular outside 0. An essential divisor over (X,0) is a divisorial valuation of the field of meromorphic functions on (X,0), whose center on any resolution of the germ is an irreducible component of the exceptional locus. The Nash map associates to each irreducible component of the space of arcs through 0 on X the unique essential divisor intersected by the strict transform of the generic arc in the component. Nash proved its injectivity and asked if it was bijective. We prove that this is the case if there exists a divisorial resolution \pi of (X,0) such that its reduced exceptional divisor carries sufficiently many \pi-ample divisors (in a sense we define). Then we apply this criterion to construct an infinite number of families of 3-dimensional examples, which are not analytically isomorphic to germs of toric 3-folds (the only class of normal 3-fold germs with bijective Nash map known before).

Affiliated with

Also associated with

No associations

Rating

Families of higher dimensional germs with bijective Nash map 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 Families of higher dimensional germs with bijective Nash map, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Families of higher dimensional germs with bijective Nash map will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-16300