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arXiv · 2412.06500

Smoothing Gorenstein toric Fano 3-folds

Alessio Corti·Paul Hacking·Andrea Petracci
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Abstract

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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Alessio Corti, Paul Hacking, Andrea Petracci. 2024-12-09. Smoothing Gorenstein toric Fano 3-folds. https://arxiv.org/abs/2412.06500

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