CalabiYau volumes and reflexive polytopes

Yang-Hui He Rak-Kyeong Seong Shing-Tung Yau

Algebraic Geometry mathscidoc:1912.43670

Communications in Mathematical Physics, 361, (1), 155-204
We study various geometrical quantities for CalabiYau varieties realized as cones over Gorenstein Fano varieties, obtained as toric varieties from reflexive polytopes in various dimensions. Focus is made on reflexive polytopes up to dimension 4 and the minimized volumes of the SasakiEinstein base of the corresponding CalabiYau cone are calculated. By doing so, we conjecture new bounds for the SasakiEinstein volume with respect to various topological quantities of the corresponding toric varieties. We give interpretations about these volume bounds in the context of associated field theories via the AdS/CFT correspondence.
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  title={CalabiYau volumes and reflexive polytopes},
  author={Yang-Hui He, Rak-Kyeong Seong, and Shing-Tung Yau},
  booktitle={Communications in Mathematical Physics},
Yang-Hui He, Rak-Kyeong Seong, and Shing-Tung Yau. CalabiYau volumes and reflexive polytopes. Vol. 361. In Communications in Mathematical Physics. pp.155-204.
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