We consider 18 families of elliptic Calabi-Yaus which arise in constructing F-theory compactifications of string vacua, and show in each case that the upper Hodge diamond of a crepant resolution of the associated Weierstrass model coincides with the upper Hodge diamond of the (blown up) projective bundle in which the crepant resolution is naturally embedded. Such results are unexpected, as each crepant resolution we consider does not satisfy the hypotheses of the Lefschetz hyperplane theorem. In light of such findings, we suspect that all elliptic Calabi-Yaus satisfy such a ‘Lefschetz-type phenomenon’.
On a Lefschetz-type phenomenon for elliptic Calabi-Yaus / Fullwood, J.; Cattaneo, A.. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2022:4(2022). [10.1007/JHEP04(2022)141]
On a Lefschetz-type phenomenon for elliptic Calabi-Yaus
Cattaneo A.
2022-01-01
Abstract
We consider 18 families of elliptic Calabi-Yaus which arise in constructing F-theory compactifications of string vacua, and show in each case that the upper Hodge diamond of a crepant resolution of the associated Weierstrass model coincides with the upper Hodge diamond of the (blown up) projective bundle in which the crepant resolution is naturally embedded. Such results are unexpected, as each crepant resolution we consider does not satisfy the hypotheses of the Lefschetz hyperplane theorem. In light of such findings, we suspect that all elliptic Calabi-Yaus satisfy such a ‘Lefschetz-type phenomenon’.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
