Abstract
We consider examples of extremal transitions between families of Calabi-Yau complete intersection threefolds in toric varieties, which are induced by toric embeddings of one toric variety into the other. We show that the toric map induced by the linear dual of the embedding induces a birational morphism between the mirror Calabi-Yau families, and in one case show that it can be extended to the full mirror transition between mirror families.
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Acknowledgments
I would like to thank the authors of the computer algebra program Macaulay2 Grayson and Stillman (2002) and its Polyhedra package Birkner (2009). I would also like to thank Nathan Ilten for helpful comments, and Mark Gross for introducing me to the problem of mirror symmetry for complete intersections in Grassmannians, as well as comments about the proof of Proposition 5.8.
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Fredrickson, K. Mirror transitions and the Batyrev-Borisov construction. Beitr Algebra Geom 56, 677–693 (2015). https://doi.org/10.1007/s13366-015-0242-x
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DOI: https://doi.org/10.1007/s13366-015-0242-x