Journal of Differential Geometry

Riemann-Roch for toric orbifolds

Victor Guillemin

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Article information

J. Differential Geom. Volume 45, Number 1 (1997), 53-73.

First available in Project Euclid: 26 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58F06
Secondary: 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx] 58F05


Guillemin, Victor. Riemann-Roch for toric orbifolds. J. Differential Geom. 45 (1997), no. 1, 53--73.

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  • [1] R. Bott and L. Tu, Differential forms in algebraic topology, Springer, New York, 1982.
  • [2] M. Brion, Points entiers dans les polyedres convexes, Ann. Sci. Ecole Norm. Sup. 21 (1988) 653-665.
  • [3] M. Brion and M. Vergne, Lattice points in simple polytopes, Preprint, May, 1995.
  • [4] S. Cappell and J. Shaneson, Characteristic classes, lattice points and Euler-Maclaurin formulae, Proc. Internat. Congr. Math. (Zurich, 1996), to appear.
  • [5] V.I. Danilov, The geometry of toric varieties, Russian Math. Surveys 33 (1978) 97-154.
  • [6] J.J. Duistermaat, V. Guillemin, E. Meinrenken and S. Wu, Symplectic reduction and Riemann-Roch for circle actions, Math. Res. Lett. 2 (1995) 259-266.
  • [7] V. Guillemin, Reduced phase spaces and Riemann-Roch, in Lie Theory and Geometry, Progr. Math. 123 (1994) 305-334.
  • [8] V. Guillemin, Kaehler structures on toric varieties, J. Differential Geom. 40 (1994) 285-309.
  • [9] V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982) 515-538.
  • [10] V. Guillemin and S. Sternberg, Homogeneous quantization and multiplicities of group representations, J. Funct. Anal. 47 (1982) 344-380.
  • [11] L. Jeffrey and F. Kirwan, On localization and Riemann-Roch numbers for symplectic quotients, Preprint, September, 1994.
  • [12] T. Kawasaki, The Riemann-Roch theorem for complex V-manifolds, Osaka J. Math. 16 (1979) 151-159.
  • [13] A. Khovanskii and J.M. Kantor, Integral points in convex polyhedra, combinatorial Riemann-Roch and generalized Maclaurin formulae, Inst. Hautes Etudes Sci. Publ. Math. (1992) 932-937.
  • [14] A. Khovanskii and S. Pukhlikov, Théoreme de Riemann-Roch pour les intégrales et les sommes de quasi-polynomes sur les polyedres virtuels, Algebra i analiz 4 (1992) 188-216.
  • [15] B. Kostant, Quantization and unitary representations, Lecture notes in Math. Vol. 170, Springer, Berlin, 1970, 87-207.
  • [16] B. Lawson and M. Michelsohn, Spin Geometry, Princeton Univ. Press, Princeton, 1989.
  • [17] S. Martin and J. Weitsman, On a conjecture of Guillemin-Sternberg, to appear.
  • [18] E. Meinrenken, On Riemann-Roch formulas for multiplicities, J. Amer. Math. Soc, to appear.
  • [19] E. Meinrenken, Symplectic surgery and the spin c-Dirac operator, Preprint, March, 1995.
  • [20] R. Morelli, Pick's theorem and the Todd class of a toric variety, Adv. Math. 100 (1993) 183-231.
  • [21] J.E. Pommersheim, Toric varieties, lattice points and Dedekind sums, Math. Ann. 295 (1993) 1-24.
  • [22] I. Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. U.S.A. 42 (1956) 359-363.
  • [23] R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction, Ann. of Math. 134 (1991) 375-422.
  • [24] B. Sturmfels, On vector partition functions, Preprint, July, 1994.
  • [25] M. Vergne, Quantification géométrique et multiplicités, CR. Acad. Sci. Paris, 319 (1994) 327-332.