Abstract
We study a toric modification of Fujiki-Oka type for cyclic quotient singularities. Especially the behavior of rational Chow rings, orbifold signatures and so on are explicitly calculated. As a result, we extend Zagier's reciprocity for higher-dimensional Dedekind sums. Namely, we define Dedekind sums with weight by using Atiyah-Singer's equivariant signature with non-isolated fixed point locus, and then prove our reciprocity among them.
Citation
Tadashi Ashikaga. "Toric modifications of cyclic orbifolds and an extended Zagier reciprocity for Dedekind sums." Tohoku Math. J. (2) 67 (3) 323 - 347, 2015. https://doi.org/10.2748/tmj/1446818556
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