All toric l.c.i.-singularities admit projective crepant resolutions

TL;DR

This paper proves that all toric l.c.i.-singularities can be resolved by projective crepant resolutions, extending known results from abelian quotient singularities using advanced toric and discrete geometric methods.

Contribution

It extends the class of singularities known to admit projective crepant resolutions to all toric l.c.i.-singularities, utilizing Nakajima's classification and specialized geometric techniques.

Findings

All toric l.c.i.-singularities admit projective crepant resolutions.

Extension of resolution results from abelian quotient singularities to all toric l.c.i.-singularities.

Use of Nakajima's classification theorem and toric geometry methods.

Abstract

It is known that the underlying spaces of all abelian quotient singularities which are embeddable as complete intersections of hypersurfaces in an affine space can be overall resolved by means of projective torus-equivariant crepant birational morphisms in all dimensions. In the present paper we extend this result to the entire class of toric l.c.i.-singularities. Our proof makes use of Nakajima's classification theorem and of some special techniques from toric and discrete geometry.