Geodesic
Calabi--Yau hypersurfaces and SU-bordism
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Topology and physics, Tome 302 (2018), pp. 287-295

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V. V. Batyrev constructed a family of Calabi–Yau hypersurfaces dual to the first Chern class in toric Fano varieties. Using this construction, we introduce a family of Calabi–Yau manifolds whose $\mathrm {SU}$-bordism classes generate the special unitary bordism ring $\varOmega ^{\mathrm {SU}}\bigl [\tfrac 12\bigr ]\cong \mathbb {Z}\bigl [\tfrac 12\bigr ][y_i\colon i\ge 2]$. We also describe explicit Calabi–Yau representatives for multiplicative generators of the $\mathrm {SU}$-bordism ring in low dimensions.
Keywords: special unitary bordism, SU-manifold, Calabi–Yau manifold, Chern number, toric Fano variety, reflexive polytope. 
@article{TM_2018_302_a12,
     author = {Ivan Yu. Limonchenko and Zhi L\"u and Taras E. Panov},
     title = {Calabi--Yau hypersurfaces and {SU-bordism}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {287--295},
     publisher = {mathdoc},
     volume = {302},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_302_a12/}
}
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Ivan Yu. Limonchenko; Zhi Lü; Taras E. Panov. Calabi--Yau hypersurfaces and SU-bordism. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Topology and physics, Tome 302 (2018), pp. 287-295. http://geodesic.mathdoc.fr/item/TM_2018_302_a12/