McKay correspondence and new Calabi-Yau threefolds

TL;DR

This paper explores crepant resolutions of quotient varieties from smooth quintic threefolds under Gorenstein group actions, using McKay correspondence to compute Hodge numbers and discover new Calabi-Yau threefolds with novel Hodge number pairs.

Contribution

It introduces new Calabi-Yau threefolds by applying McKay correspondence to quotient varieties, expanding known Hodge number pairs.

Findings

Computed Hodge numbers for new Calabi-Yau threefolds

Identified novel pairs of Hodge numbers

Enhanced understanding of crepant resolutions in algebraic geometry

Abstract

In this note, we consider crepant resolutions of the quotient varieties of smooth quintic threefolds by Gorenstein group actions. We compute their Hodge numbers via McKay correspondence. In this way, we find some new pairs $(h^{1,1},\;h^{2,1})$ of Hodge numbers of Calabi-Yau threefolds.