arXiv subjects

Shu Nimura

Publications and source records attributed to Shu Nimura.

2 recordsLinked to original sources

arXiv2026

Ishii's conjecture and Bridgeland stability conditions for dihedral reflection groups

We provide a new proof of Ishii's conjecture for any dihedral reflection group $G\subset GL_2(\mathbb{C})$ from the viewpoint of Bridgeland stability conditions. Our strategy is to reduce the problem, via the derived McKay correspondence, to a geometric construction of Bridgeland stability conditions on the root stack of the maximal resolution along the strict transform of the discriminant divisor.

math.AG↗

arXiv2025

Derived McKay correspondence for real reflection groups of rank three

We describe the derived McKay correspondence for real reflection groups of rank $3$ in terms of a maximal resolution of the logarithmic pair consisting of the quotient variety and the discriminant divisor with coefficient $\frac{1}{2}$. As an application, we verify a conjecture by Polishchuk and Van den Bergh on the existence of a certain semiorthgonal decomposition of the equivariant derived category into the derived categories of affine spaces for any real reflection group of rank $3$.

math.AG↗