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Smoothing Gorenstein toric Fano 3-folds

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arxiv 2412.06500 v1 pith:KUHS2MZH submitted 2024-12-09 math.AG

Alessio Corti , Paul Hacking , Andrea Petracci This is my paper · ORCID
classification math.AG
keywords smoothingfanogorensteinresulttoricadmissibleamountsbetti
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We introduce admissible Minkowski decomposition data (amd) for a 3-dimensional reflexive polytope P. This notion is defined purely in terms of the combinatorics of P. Denoting by X the Gorenstein toric Fano 3-fold whose fan is the spanning fan (a.k.a. face fan) of P, our first result states that amd for P determine a smoothing of X. Our second result amounts to an effective recipe for computing the Betti numbers of the smoothing.

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Cited by 1 Pith paper

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  1. Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$

    math.AG 2025-06 reject novelty 6.0 of 10

    The cohomology and intersection form of smooth hypersurfaces in weighted projective spaces are computed explicitly via Alexander duality and a covering by ordinary projective space.

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