Derived McKay correspondence for real reflection groups of rank three

2025/04/02 by Ishii, Akira, Nimura, Shu
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.01387

Abstract

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 (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.

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