Calabi-Yau compactifications and mirror symmetry are conjecturally extended to non-algebraic toric spaces using Laurent deformations and the 'intrinsic limit' completion.
On a Residue Representation of Deformation, Koszul and Chiral Rings
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abstract
A residue-theoretic representation is given for massless matter fields in (quotients) of (weighted) \CY\ complete intersection models and the corresponding chiral operators in \LGO{s}. The well known polynomial deformations are thus generalized and the universal but somewhat abstract Koszul computations acquire a concrete realization and a general but more heuristic reinterpretation. A direct correspondence with a BRST-type analysis of constrained systems also emerges naturally.
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Beyond Algebraic Superstring Compactification
Calabi-Yau compactifications and mirror symmetry are conjecturally extended to non-algebraic toric spaces using Laurent deformations and the 'intrinsic limit' completion.