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We produce simply-connected, minimal, symplectic Lefschetz fibrations realizing all the lattice points in the symplectic geography plane below the Noether line. This provides asymplecticextension of the classical works populating the complex geography plane with holomorphic Lefschetz fibrations. Our examples are obtained by rationally blowing down Lefschetz fibrations with clustered nodal fibers, the total spaces of which are potentially new homotopy elliptic surfaces. Similarly, clustering nodal fibers on higher genera Lefschetz fibrations on standard rational surfaces, we get rational blowdown configurations that yield new constructions of small symplectic exotic –manifolds. We present an example of a construction of a minimal symplectic exotic through this procedure applied to a genus– fibration.
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Calabi-Yau Genus-One Fibrations and Twisted Dimensional Reductions of F-theory
In this brief note we explore the space of genus one and elliptic fibrations within CY manifolds, their organizing principles, and how they relate to the set of all CY manifolds. We provide examples of genus one fibered manifolds that exhibit different Hodge numbers -- and physically lead to different gauge groups - than their Jacobian fibrations. We suggest a physical mechanism for understanding this difference in twisted circle reductions of 6-dimensional compactifications of F-theory.
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- Award ID(s):
- 2014086
- PAR ID:
- 10447672
- Date Published:
- Journal Name:
- Proceedings of the Nankai Symposium on Mathematical Dialogues
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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