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Mirror Transitions and the Batyrev-Borisov construction

2012/12/24 by Karl Fredrickson, Fredrickson, Karl
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1212.5904

openalex publication_date 2012/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. Note: this version uses a different approach to give a shorter proof of the same result. Also, Lemma 5.8 in the previous versions is definitely wrong.

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