Geodesic
Ice cream and orbifold Riemann--Roch
Izvestiya. Mathematics , Tome 77 (2013) no. 3, pp. 461-486

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We give an orbifold Riemann–Roch formula in closed form for the Hilbert series of a quasismooth polarized $n$-fold $(X,D)$, under the assumption that $X$ is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of $\mathrm{K3}$ surfaces and Calabi–Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications. Bibliography: 22 titles.
Keywords: orbifold, orbifold Riemann–Roch, Dedekind sum, Hilbert series, weighted projective varieties. 
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     author = {A. Buckley and M. Reid and S. Zhou},
     title = {Ice cream and orbifold {Riemann--Roch}},
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A. Buckley; M. Reid; S. Zhou. Ice cream and orbifold Riemann--Roch. Izvestiya. Mathematics , Tome 77 (2013) no. 3, pp. 461-486. http://geodesic.mathdoc.fr/item/IM2_2013_77_3_a2/