The regularizing fractional-transformation conjecture for VEX-multitope Calabi–Yau hypersurfaces

Let a Calabi–Yau Laurent hypersurface be encoded by a VEX multitope of anticanonical sections. A fractional transformation is a change of variables that may involve roots and powers, and a regular defining polynomial is a sum of monomials with only non-negative powers. A complete intersection is of general type when its canonical class has the corresponding general-type sign.

Regularizing fractional-transformation conjecture. All such Calabi–Yau Laurent hypersurfaces are also describable, via suitable fractional transformations, in terms of general-type complete intersections of hypersurfaces in projective spaces with strictly regular defining polynomials.

This would give an algebraic reinterpretation of the intrinsic-limit completion by replacing Laurent equations with regular equations of general type. The source presents it as a proposal and provides no proof, so it remains open.

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Primary source

Tristan Hübsch, “Beyond Algebraic Superstring Compactification”, arXiv:2502.08002 (2025).

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