Graph hypersurfaces and a dichotomy in the Grothendieck ring

Details Graph hypersurfaces and a dichotomy in the Grothendieck ring Graph hypersurfaces and a dichotomy in the Grothendieck ring

2010-05-25

arxiv.org/abs/1005.4470v1

Lett.Math.Phys.95:223-232,2011

Mathematics

Algebraic Geometry

8 pages, LaTeX

Scientific paper

10.1007/s11005-011-0461-5

The subring of the Grothendieck ring of varieties generated by the graph hypersurfaces of quantum field theory maps to the monoid ring of stable birational equivalence classes of varieties. We show that the image of this map is the copy of Z generated by the class of a point. Thus, the span of the graph hypersurfaces in the Grothendieck ring is nearly killed by setting the Lefschetz motive L to zero, while it is known that graph hypersurfaces generate the Grothendieck ring over a localization of Z[L] in which L becomes invertible. In particular, this shows that the graph hypersurfaces do not generate the Grothendieck ring prior to localization. The same result yields some information on the mixed Hodge structures of graph hypersurfaces, in the form of a constraint on the terms in their Deligne-Hodge polynomials.

Affiliated with

Also associated with

No associations

Rating

Graph hypersurfaces and a dichotomy in the Grothendieck ring 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 Graph hypersurfaces and a dichotomy in the Grothendieck ring, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Graph hypersurfaces and a dichotomy in the Grothendieck ring will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-297144