2016/06/23 by Per Berglund, Tristan Hübsch, Tristan Hubsch
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algorithm #Artificial intelligence #Calabi–Yau manifold #Cohomology #Complete intersection #Computation #Computer science #Embedding #Geometry and complex manifolds #Intersection (aeronautics) #Intersection homology #Mathematics #Projective space #Projective test #Pure mathematics #Space (punctuation) #hep-th #math.AG
paper · pdf · doi:10.4310/atmp.2018.v22.n2.a1
published as Adv. Theor. Math. Phys. 22 (2) (2018) 261-303 · 32 pages, 2 figures
arxiv created 2016/06/23 · openalex publication_date 2018/01/01 · arxiv updated 2020/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the construction of Calabi-Yau varieties recently generalized to where the defining equations may have negative degrees over some projective space factors in the embedding space. Within such "generalized complete intersection" Calabi-Yau ("gCICY") three-folds, we find several sequences of distinct manifolds. These include both novel elliptic and K3-fibrations and involve Hirzebruch surfaces and their higher dimensional analogues. En route, we generalize the standard techniques of cohomology computation to these generalized complete intersection Calabi-Yau varieties.