Thomas Huettemann
Published 2006-07-19, updated 2006-07-26Version 2
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.
Comments: 15 pages; uses Paul Taylor's "diagrams" and "QED" macro packages; v2: "noetherian" hypothesis removed, minor typos corrected
Journal: Homology, Homotopy and Applications 9 (2007), No. 2, pp. 321-336
A degenerate version of Brion's formula
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