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math.AG2026
Doubly isolated Batyrev mirror pairs and non-smoothable Calabi-Yau threefolds
Bernd Johannes Wuebben
We classify reflexive four-polytopes for which the generic anticanonical hypersurfaces associated with the face fans of the polytope and its polar both have at most isolated singul…
math.AG2026
Deformations of toric pairs and the smoothing of Batyrev Calabi-Yau threefolds
Bernd Johannes Wuebben
Let be a reflexive four-polytope with primitive edges. We construct deformations of the toric fourfold defined by its face fan that smooth the singularities of a generic antica…
math.AG2026
Non-smoothable Calabi-Yau threefolds from reflexive polytopes
Bernd Johannes Wuebben
We construct projective Calabi-Yau threefolds with isolated Gorenstein canonical singularities that admit no smoothing, as anticanonical hypersurfaces in Gorenstein Fano toric four…