Ice cream and orbifold Riemann–Roch

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.
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