Fetching the paper…
Reading the bibliography…
We apply mirror symmetry to the problem of counting holomorphic rational curves in a Calabi-Yau threefold X with Z_3 x Z_3 Wilson lines.
C. T. C. Wall, “Classification Problems in Differential Topology. V: On Certain 6- manifolds,” Invent. Math
1967
Earlier work this paper cites.
V. Danilov, “Geometry of Toric Varieties,” Russ. Math. Surv
1978
Earlier work this paper cites.
C. Schoen, “On fiber products of rational elliptic surfaces with section,” Math. Z
1988
Earlier work this paper cites.
P. S. Aspinwall, C. A. Lutken, and G. G. Ross, “Construction and couplings of mirror manifolds,” Phys. Lett
1990
Earlier work this paper cites.
L. J. Billera, P. Filliman, and B. Sturmfels, “Constructions and complexity of secondary polytopes,” Adv. Math
1990
Earlier work this paper cites.
P. Candelas, X. C. De La Ossa, P. S. Green, and L. Parkes, “A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory,” Nucl. Phys
1991
Earlier work this paper cites.
V. V. Batyrev, “On the classification of smooth projective toric varieties,” Tohoku Math. J., II. Ser
1991
Earlier work this paper cites.
V. V. Batyrev, “Quantum Cohomology Rings of Toric Manifolds,” Astérisque
1993
Earlier work this paper cites.
P. S. Aspinwall and D. R. Morrison, “Chiral rings do not suffice: N=(2,2) theories with nonzero fundamental group,” Phys. Lett
1994
Earlier work this paper cites.
V. V. Batyrev, “Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties,” J. Alg. Geom
1994
Earlier work this paper cites.
M. Kreuzer, “The Mirror map for invertible LG models,” Phys. Lett
1994
Earlier work this paper cites.
Mathematics: Theory & Applications. Birkhäuser Boston Inc., Boston, MA, 1994
I. M. Gel ′ · 1994
Earlier work this paper cites.
S. Ferrara, J. A. Harvey, A. Strominger, and C. Vafa, “Second quantized mirror symmetry,” Phys. Lett
1995
Earlier work this paper cites.
P. Berglund, S. H. Katz, and A. Klemm, “Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties,” Nucl. Phys
1995
Earlier work this paper cites.
S. Hosono, A. Klemm, S. Theisen, and S.-T. Yau, “Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces,” Nucl. Phys
1995
Earlier work this paper cites.
D. A. Cox, “The Homogeneous Coordinate Ring of a Toric Variety,” J. Algebr. Geom
1995
Earlier work this paper cites.
P. S. Aspinwall, D. R. Morrison, and M. Gross, “Stable singularities in string theory,” Commun. Math. Phys
1996
Earlier work this paper cites.
P. S. Aspinwall, “An N=2 Dual Pair and a Phase Transition,” Nucl. Phys
1996
Cited alongside, same era.
de Gruyter, Berlin, 1996
V. V. Batyrev and L. A. Borisov, “On Calabi-Yau complete intersections in toric varieties,” in Higher-dimensional complex varieties (Trento, 1994) · 1996
Cited alongside, same era.
V. V. Batyrev and L. A. Borisov, “Mirror duality and string-theoretic Hodge numbers,” Invent. Math
1996
Cited alongside, same era.
A. B. Givental, “Equivariant Gromov-Witten invariants,” Internat. Math. Res. Notices
1996
Cited alongside, same era.
Y. Ruan, “Topological sigma model and Donaldson-type invariants in Gromov theory,” Duke Math. J
1996
Cited alongside, same era.
S. Hosono, M. Saito, and J. Stienstra, “On the mirror symmetry conjecture for Schoen’s Calabi-Yau 3-folds,” alg-geom/9709027 . Given at Taniguchi Symposium on Integrable Systems and Algebraic Geometry, Kyoto, Japan, 7-11 Jul 1997
M. Kreuzer and H. Skarke, “Complete classification of reflexive polyhedra in four dimensions,” Adv. Theor. Math. Phys
2002
Later among the works it cites.
J. A. Wiśniewski, “Toric Mori theory and Fano manifolds,” Séminaires & Congrès
2002
Later among the works it cites.
E. I. Buchbinder, R. Donagi, and B. A. Ovrut, “Superpotentials for vector bundle moduli,” Nucl. Phys
2003
Later among the works it cites.
V. Braun, B. A. Ovrut, T. Pantev, and R. Reinbacher, “Elliptic Calabi-Yau threefolds with Z(3) x Z(3) Wilson lines,” JHEP
2004
Later among the works it cites.
E. I. Buchbinder and B. A. Ovrut, “Vacuum stability in heterotic M-theory,” Phys. Rev
2004
Later among the works it cites.
M. Kreuzer and H. Skarke, “PALP: A Package for analyzing lattice polytopes with applications to toric geometry,” Comput. Phys. Commun
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1997
Cited alongside, same era.
Amer. Math. Soc., Providence, RI, 1997
M. Gross, “The deformation space of Calabi-Yau n n -folds with canonical singularities can be obstructed,” in Mirror symmetry, II · 1997
Cited alongside, same era.
World Scientific, Singapore, 1998
J. Stienstra, “Resonant Hypergeometric Systems and Mirror Symmetry,” in Integrable systems and algebraic geometry · 1998
Cited alongside, same era.
Birkhäuser Boston, Boston, MA, 1998
A. B. Givental, “A mirror theorem for toric complete intersections,” in Topological field theory, primitive forms and related topics (Kyoto, 1996) · 1998
Cited alongside, same era.
American Mathematical Society, Providence, RI, 1999
D. A. Cox and S. Katz, Mirror symmetry and algebraic geometry · 1999
Cited alongside, same era.
S. Hosono, M. H. Saito, and A. Takahashi, “Holomorphic anomaly equation and BPS state counting of rational elliptic surface,” Adv. Theor. Math. Phys
1999
Cited alongside, same era.
E. Lima, B. A. Ovrut, J. Park, and R. Reinbacher, “Non-perturbative superpotential from membrane instantons in heterotic M-theory,” Nucl. Phys
2001
Cited alongside, same era.
2004
Later among the works it cites.
V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “A heterotic standard model,” Phys. Lett
2005
Later among the works it cites.
V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “A standard model from the E(8) x E(8) heterotic superstring,” JHEP
2005
Later among the works it cites.
A. Klemm, M. Kreuzer, E. Riegler, and E. Scheidegger, “Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections,” JHEP
2005
Later among the works it cites.
http://www.singular.uni-kl.de
G.-M. Greuel, G. Pfister, and H. Schönemann, “ Singular · 2005
Later among the works it cites.
V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “The exact MSSM spectrum from string theory,” JHEP
2006
Later among the works it cites.
V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “Vector bundle extensions, sheaf cohomology, and the heterotic standard model,” Adv. Theor. Math. Phys
2006
Later among the works it cites.
V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “Heterotic standard model moduli,” JHEP
2006
Later among the works it cites.
V. Braun, Y.-H. He, and B. A. Ovrut, “Yukawa couplings in heterotic standard models,” JHEP
2006
Later among the works it cites.
V. Braun, Y.-H. He, and B. A. Ovrut, “Stability of the minimal heterotic standard model bundle,” JHEP
2006
Later among the works it cites.
V. Braun and B. A. Ovrut, “Stabilizing moduli with a positive cosmological constant in heterotic M-theory,” JHEP
2006
Later among the works it cites.