Given a polarized variety , we can associate a graded ring and a Hilbert series. Assume is an ample Cartier divisor, and is quasi smooth and projectively Gorenstein, we give a parsing formula for the Hilbert series according to their singularities. Here we allow the variety to have singularities of dimension , that is, both singularities of dimension and singular points, extending a 2013 result of Buckley, Reid and the author about varieties with only isolated singularities.
"Dedekind sums and parsing of Hilbert series." J. Commut. Algebra 13 (2) 281 - 304, Summer 2021. https://doi.org/10.1216/jca.2021.13.281