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The web of Calabi-Yau hypersurfaces in toric varieties. (English) Zbl 0896.14026
Summary: Recent results on duality between string theories and connectedness of their moduli spaces seem to go a long way toward establishing the uniqueness of an underlying theory. For the large class of Calabi-Yau 3-folds that can be embedded as hypersurfaces in toric varieties the proof of mathematical connectedness via singular limits is greatly simplified by using polytopes that are maximal with respect to certain single or multiple weight systems. We identify the multiple weight systems occurring in this approach. We show that all of the corresponding Calabi-Yau manifolds are connected among themselves and to the web of CICYs (= complete intersection Calabi-Yau). This almost completes the proof of connectedness for toric Calabi-Yau hypersurfaces.

MSC:
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14J30 \(3\)-folds
14C21 Pencils, nets, webs in algebraic geometry
14M10 Complete intersections
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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