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arXiv · 2504.06810

On the exceptional set of crepant resolutions of abelian singularities

Ugo Bruzzo·Fábio Arceu Ferreira
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Abstract

Let G be a finite abelian subgroup of SL(n,C), and suppose there exists a toric crepant resolution phi: X -- > C^n/G. We prove that for each component E of the exceptional set of phi there exists an open subset U of X that contains E and is isomorphic to the total space of the canonical bundle of E. This contributes to the collection of results aimed at solving a classical problem, i.e., to determine which submanifolds of a complex manifold have a neighborhood isomorphic to a neighborhood of the zero section of their normal bundle.

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Ugo Bruzzo, Fábio Arceu Ferreira. 2025-04-09. On the exceptional set of crepant resolutions of abelian singularities. https://arxiv.org/abs/2504.06810

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