On extremal transitions of Calabi-Yau threefolds and the singularity of the associated 7-space from rolling

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dc.creatorBraun, Volker
dc.creatorLiu, Chien-Hao
dc.date1998-01-27
dc.date1998-12-18
dc.date.accessioned2026-07-07T04:24:10Z
dc.date.available2026-07-07T04:24:10Z
dc.descriptionM-theory compactification leads one to consider 7-manifolds obtained by rolling Calabi-Yau threefolds in the web of Calabi-Yau moduli spaces. The resulting 7-space in general has singularities governed by the extremal transition undergone. After providing some background in Sec. 1, the simplest case of conifold transitions is studied in Sec. 2. In Sec. 3 we employ topological methods, Smale's classification theorem of smooth simply-connected spin closed 5-manifolds, and a computer code in the Appendix to understand the 5-manifolds that appear as the link of the singularity of a singuler Calabi-Yau threefolds from a Type II primitive contraction of a smooth one. From this we obtain many locally admissible extremal transition pairs of Calabi-Yau threefolds, listed in Sec. 4. Their global realization will require further study. As a mathematical byproduct in the pursuit of the subject, we obtain a formula to compute the topology of the boundary of the tubular neighborhood of a Gorenstein rational singular del Pezzo surface embedded in a smooth Calabi-Yau threefold as a divisor.
dc.description38 pages, 7 Postscript figures. A computer code by V.B. is added and used to check and select possible local admissible pairs of extremal transitions in the previous version by C.-H.L
dc.identifierhttps://arxiv.org/abs/hep-th/9801175
dc.identifierhttp://arxiv.org/abs/hep-th/9801175
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/55307
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subjectAlgebraic Topology
dc.titleOn extremal transitions of Calabi-Yau threefolds and the singularity of the associated 7-space from rolling
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