English

Smoothing Gorenstein toric Fano 3-folds

Algebraic Geometry 2024-12-10 v1

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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Cite

@article{arxiv.2412.06500,
  title  = {Smoothing Gorenstein toric Fano 3-folds},
  author = {Alessio Corti and Paul Hacking and Andrea Petracci},
  journal= {arXiv preprint arXiv:2412.06500},
  year   = {2024}
}

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54 pages