Crepant Terminalisations and Orbifold Euler Numbers for SL(4) Singularities

1996/10/01 by Alexander V. Sardo Infirri, Infirri, Alexander V. Sardo · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.alg-geom/9610001

Abstract

Let X and Y be two analytic canonical Gorenstein orbifolds. A resolution of singularities Y→ X is called an Euler resolution if Y and X have the same orbifold Euler number. If Y is only terminal rather than smooth, it is called an Euler terminalisation. It is proved that Euler terminalisations exist for toric varieties in any dimension, for 4-dimensional toroidal varieties, and for singularities \C⁴/G where G belongs to certain classes of \SL(4) subgroups. The method of proof is expected to be applicable to a sizeable number of finite \SL(4) subgroups and to lead to a generalisation of the Dixon-Harvey-Vafa-Witten orbifold Euler number conjecture to dimension~4.

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