Mathematics – Combinatorics
Scientific paper
2006-07-19
Homology, Homotopy and Applications 9 (2007), No. 2, pp. 321-336
Mathematics
Combinatorics
15 pages; uses Paul Taylor's "diagrams" and "QED" macro packages; v2: "noetherian" hypothesis removed, minor typos corrected
Scientific paper
A subset K of R^n gives rise to a formal Laurent series with monomials corresponding to lattice points in K. Under suitable hypotheses, this series represents a rational function R(K). Michel Brion has discovered a surprising formula relating the rational function R(P) of a lattice polytope P to the sum of rational functions corresponding to the supporting cones subtended at the vertices of P. The result is re-phrased and generalised in the language of cohomology of line bundles on complete toric varieties. Brion's formula is the special case of an ample line bundle on a projective toric variety. - The paper also contains some general remarks on the cohomology of torus-equivariant line bundles on complete toric varieties, valid over noetherian ground rings.
No associations
LandOfFree
A cohomological interpretation of Brion's formula 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 A cohomological interpretation of Brion's formula, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A cohomological interpretation of Brion's formula will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-625836