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arXiv · 2601.05634

Special vs Essential

Yukari Ito·Kohei Sato·Yusuke Sato
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Abstract

We show a correspondence between the compact exceptional curves and divisors on $G-{\rm Hilb}(\mathbf{C}^3)$ and some non-trivial irreducible representations of $G \subset GL(n,C)$ which are special (or essential). Moreover, we provide an explicit construction of the small resolution of $G-{\rm Hilb}(\mathbf{C}^3)$ and, using this resolution, we construct a correspondence between special and essential representations. These results are an extension of ``Special McKay correspondence'' and ``Reid's recipe''.

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Yukari Ito, Kohei Sato, Yusuke Sato. 2026-01-09. Special vs Essential. https://arxiv.org/abs/2601.05634

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