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We study the quantum geometry of the class of Calabi-Yau threefolds, which are elliptic fibrations over a two-dimensional toric base.
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V. Batyrev, “Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties,” J. Algebraic Geom. 3 (1994) 493-535
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M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, “Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes,” Commun. Math. Phys. 165
1994
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P. Candelas, X. De La Ossa, A. Font, S. H. Katz and D. R. Morrison, “Mirror symmetry for two parameter models. 1.,” Nucl. Phys. B 416
1994
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C. Vafa and E. Witten, A strong coupling test of S duality,
1994
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K. Yoshioka, The Betti numbers of the moduli space of stable sheaves of rank 2 on ℙ 2 \mathbb{P}^{2}
1994
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S. Hosono, A. Klemm, S. Theisen and S. -T. Yau, “Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces,” Commun. Math. Phys. 167
1995
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S. Hosono, A. Klemm, S. Theisen, S. -T. Yau, “Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces,” Nucl. Phys. B433
1995
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M. Kaneko and D. Zagier, A generalized Jacobi theta function and quasi modular forms. in The moduli space of curves
1995
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K. Yoshioka, The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface
1995
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E. Witten, “Phase transitions in M theory and F theory,” Nucl. Phys. B 471
1996
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D. Huybrechts and M. Lehn, “The geometry of moduli spaces of sheaves,” (1996)
1996
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B. H. Lian, S. -T. Yau, “Arithmetic properties of mirror map and quantum coupling,” Commun. Math. Phys. 176
1996
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K. Yoshioka, The chamber structure of polarizations and the moduli of stable sheaves on a ruled surface
1996
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S. H. Katz, A. Klemm and C. Vafa, “Geometric engineering of quantum field theories,” Nucl. Phys. B 497
1997
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W. Lerche, P. Mayr, N. P. Warner, “Noncritical strings, Del Pezzo singularities and Seiberg-Witten curves,” Nucl. Phys. B499
1997
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J. M. Maldacena, A. Strominger and E. Witten, “Black hole entropy in M theory,” JHEP 9712
1997
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P. Mayr, Nucl. Phys. B 494
1997
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J. A. Minahan, D. Nemeschansky, N. P. Warner, “Investigating the BPS spectrum of noncritical E(n) strings,” Nucl. Phys. B508
1997
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L. Göttsche, D. Zagier, Jacobi forms and the structure of Donaldson invariants for 4-manifolds with b + = 1 b_{+}=1 ,
1998
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A. Klemm, B. Lian, S. S. Roan and S. -T. Yau, “Calabi-Yau fourfolds for M theory and F theory compactifications,” Nucl. Phys. B 518
1998
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J. A. Minahan, D. Nemeschansky, N. P. Warner, “Partition functions for BPS states of the noncritical E(8) string,” Adv. Theor. Math. Phys. 1
I. Bena, D. -E. Diaconescu and B. Florea, “Black string entropy and Fourier-Mukai transform,” JHEP 0704
2007
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D. Gaiotto, A. Strominger and X. Yin, “The M5-Brane Elliptic Genus: Modularity and BPS States,” JHEP 0708
2007
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D. Gaiotto and X. Yin, “Examples of M5-Brane Elliptic Genera,” JHEP 0711
2007
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A. Klemm and R. Pandharipande, “Enumerative geometry of Calabi-Yau 4-folds,” Commun. Math. Phys. 281
2008
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J. Manschot, “On the space of elliptic genera,” Commun. Num. Theor. Phys. 2
2008
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1998
Cited alongside, same era.
J. A. Minahan, D. Nemeschansky, C. Vafa and N. P. Warner, E-strings and 𝒩 = 4 {\cal N}=4 topological Yang-Mills theories
1998
Cited alongside, same era.
T. M. Chiang, A. Klemm, S. -T. Yau and E. Zaslow, Adv. Theor. Math. Phys. 3
1999
Cited alongside, same era.
L. Göttsche, Theta functions and Hodge numbers of moduli spaces of sheaves on rational surfaces,
1999
Cited alongside, same era.
S. Hosono, M. H. Saito, A. Takahashi, “Holomorphic anomaly equation and BPS state counting of rational elliptic surface,” Adv. Theor. Math. Phys. 3
1999
Cited alongside, same era.
W.-P. Li and Z. Qin, On blowup formulae for the S S -duality conjecture of Vafa and Witten,
1999
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K. Yoshioka, Euler characteristics of SU(2) instanton moduli spaces on rational elliptic surfaces,
1999
Cited alongside, same era.
2009
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V. Bouchard, A. Klemm, M. Marino and S. Pasquetti, “Remodeling the B-model,” Commun. Math. Phys. 287
2009
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M. -x. Huang, A. Klemm and S. Quackenbush, “Topological string theory on compact Calabi-Yau: Modularity and boundary conditions,” Lect. Notes Phys. 757
2009
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2010
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T. Dimofte and S. Gukov, Refined, Motivic, and Quantum
2010
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B. Haghighat and A. Klemm, JHEP 1001
2010
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J. Manschot, Stability and duality in 𝒩 = 2 {\cal N}=2 supergravity,
2010
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F. Denef and G. W. Moore, “Split states, entropy enigmas, holes and halos,” JHEP 1111
2011
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J. Manschot, “Wall-crossing of D4-branes using flow trees,” Adv. Theor. Math. Phys. 15
2011
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2011
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J. Manschot, B. Pioline and A. Sen, “Wall Crossing from Boltzmann Black Hole Halos,” JHEP 1107
2011
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2011
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