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We show that genus-one fibrations lacking a global section fit naturally into the geometric moduli space of Weierstrass models.
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A. Grassi, “Log contractions and equidimensional models of elliptic threefolds,” J. Algebraic Geom. 4
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B. R. Greene, D. R. Morrison and A. Strominger, “Black hole condensation and the unification of string vacua,” Nucl. Phys. B 451
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C. Vafa, “Evidence for F-Theory,” Nucl. Phys. B 469
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D. R. Morrison and C. Vafa, “ Compactifications of F-Theory on Calabi–Yau Threefolds – I,” Nucl. Phys. B 473
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D. R. Morrison and C. Vafa, “Compactifications of F-Theory on Calabi–Yau Threefolds – II,” Nucl. Phys. B 476
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S. Katz, D. R. Morrison, and M. R. Plesser, “Enhanced gauge symmetry in type II string theory,” Nucl. Phys. B 477
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M. Bershadsky, K. Intriligator, S. Kachru, D. R. Morrison, V. Sadov, and C. Vafa, “Geometric singularities and enhanced gauge symmetries,” Nucl. Phys. B 481
1996
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E. Witten, “Phase transitions in M M -theory and F F -theory,” Nucl. Phys. B 471
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C.-L. Wang, “On the incompleteness of the Weil-Petersson metric along degenerations of Calabi-Yau manifolds,” Math. Res. Lett. 4
1997
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A. Klemm, B. Lian, S. S. Roan, S. -T. Yau, “Calabi-Yau fourfolds for M theory and F theory compactifications,” Nucl. Phys. B 518
1998
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P. S. Aspinwall and D. R. Morrison, “Non-simply-connected gauge groups and rational points on elliptic curves,” JHEP 9807
1998
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D. R. Morrison, “Wilson Lines in F-Theory.” Lecture at Harvard University, 8 January 1999 (unpublished)
1999
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J. de Boer, R. Dijkgraaf, K. Hori, A. Keurentjes, J. Morgan, D. R. Morrison, and S. Sethi, “Triples, Fluxes, and Strings,” Adv. Theor. Math. Phys. 4
2001
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2012
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D. S. Park, “Anomaly Equations and Intersection Theory,” JHEP 1201
2012
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2012
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2012
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D. R. Morrison and W. Taylor, “Matter and singularities,” JHEP 1201
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S. Y. An, S. Y. Kim, D. C. Marshall, S. H. Marshall, W. G. McCallum, and A. R. Perlis, “Jacobians of genus one curves,” J. Number Theory 90
2001
Cited alongside, same era.
M. Kreuzer and H. Skarke, “Complete classification of reflexive polyhedra in four-dimensions,” Adv. Theor. Math. Phys. 4
2002
Cited alongside, same era.
N. Nakayama, “Global structure of an elliptic fibration,” Publ. RIMS, Kyoto Univ. 38
2002
Cited alongside, same era.
A. Grassi, D. R. Morrison, “Group representations and the Euler characteristic of elliptically fibered Calabi-Yau threefolds”, J. Algebraic Geom. 12
2003
Cited alongside, same era.
H. Jockers and J. Louis, “D-terms and F-terms from D7-brane fluxes,” Nucl. Phys. B 718
2005
Cited alongside, same era.
M. Buican, D. Malyshev, D. R. Morrison, H. Verlinde and M. Wijnholt, “D-branes at Singularities, Compactification, and Hypercharge,” JHEP 0701
2007
Cited alongside, same era.
V. Kumar and W. Taylor, “A Bound on 6D N=1 supergravities,” JHEP 0912
2009
Cited alongside, same era.
2012
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D. R. Morrison and W. Taylor, “Toric bases for 6D F-theory models,” Fortsch. Phys. 60
2012
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W. Taylor, “On the Hodge structure of elliptically fibered Calabi-Yau threefolds,” JHEP 1208
2012
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A. Collinucci and R. Savelli, “On Flux Quantization in F-Theory,” JHEP 1202
2012
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2012
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2012
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T. W. Grimm and H. Hayashi, “F-theory fluxes, Chirality and Chern-Simons theories,” JHEP 1203
2012
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2012
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2013
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2013
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V. Braun, T. W. Grimm and J. Keitel, “New Global F-theory GUTs with U(1) symmetries,” JHEP 1309
2013
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2013
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2013
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A. Grassi, J. Halverson and J. L. Shaneson, “Matter From Geometry Without Resolution,” JHEP 1310
2013
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2014
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2014
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2014
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