# On the Calabi–Yau Compactifications of Toric Landau–Ginzburg Models for Fano Complete Intersections

@article{Przyjalkowski2017OnTC, title={On the Calabi–Yau Compactifications of Toric Landau–Ginzburg Models for Fano Complete Intersections}, author={Victor Przyjalkowski}, journal={Mathematical Notes}, year={2017}, volume={103}, pages={104-110} }

It is well known that Givental’s toric Landau–Ginzburg models for Fano complete intersections admit Calabi–Yau compactifications. We give an alternative proof of this fact. As a consequence of this proof, we obtain a description of the fibers over infinity of the compactified toric Landau–Ginzburg models.

## 11 Citations

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We consider the procedure that constructs log Calabi-Yau compactifications of weak Landau-Ginzburg models of Fano varieties. We apply it to del Pezzo surfaces and coverings of projective spaces of…

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### Nef partitions for codimension 2 weighted complete intersections

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We prove that a smooth well-formed Fano weighted complete intersection of codimension 2 has a nef partition. We discuss applications of this fact to
Mirror Symmetry. In particular we list all nef…

### Hodge level for weighted complete intersections

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We give lower bounds for Hodge numbers of smooth well formed Fano weighted complete intersections. In particular, we compute their Hodge level, that is, the maximal distance between non-trivial Hodge…

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We survey the approach to mirror symmetry via Laurent polynomials, outlining some of the main conjectures, problems, and questions related to the subject. We discuss: how to construct Landau–Ginzburg…

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We suggest the procedure that constructs a log Calabi–Yau compactification of weak Landau–Ginzburg model of a Fano variety. We apply the suggestion for del Pezzo surfaces and coverings of projective…

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We prove that smooth Fano threefolds have toric Landau- Ginzburg models. More precisely, we prove that their Landau-Ginzburg models, represented as Laurent polynomials, admit compactifications to…

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Abstract For an appropriate class of Fano complete intersections in toric varieties, we prove that there is a concrete relationship between degenerations to specific toric subvarieties and…

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A common way to construct Fano varieties in higher dimensions is to represent them as complete intersections in familiar varieties such as toric varieties or Grassmannians. The well-known Givental…