Advances in Theoretical and Mathematical Physics

Volume 22 (2018)

Number 2

On Calabi–Yau generalized complete intersections from Hirzebruch varieties and novel $K3$-fibrations

Pages: 261 – 303



Per Berglund (Department of Physics, University of New Hampshire, Durham, N.H., U.S.A.)

Tristan Hübsch (Department of Physics & Astronomy, Howard University, Washington, D.C., U.S.A.)


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.

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