Transpolar pairs involving VEX multitopes yield smooth toric spaces whose Chern classes satisfy Todd-Hirzebruch identities and belong to deformation families of generalized complete intersections.
The web of Calabi-Yau hypersurfaces in toric varieties
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abstract
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 CICY's. This almost completes the proof of connectedness for toric Calabi-Yau hypersurfaces.
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A roadmap paper describing potential applications of numerical Ricci-flat Calabi-Yau metrics to heterotic string phenomenology and mathematical questions in special geometry.
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Chern Characteristics and Todd-Hirzebruch Identities for Transpolar Pairs of Toric Spaces
Transpolar pairs involving VEX multitopes yield smooth toric spaces whose Chern classes satisfy Todd-Hirzebruch identities and belong to deformation families of generalized complete intersections.
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What to do with a Ricci-flat Calabi--Yau metric?
A roadmap paper describing potential applications of numerical Ricci-flat Calabi-Yau metrics to heterotic string phenomenology and mathematical questions in special geometry.