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FJRW rings and LandauGinzburg Mirror Symmetry. arXiv:0906.0796v1
"... for BG. ii ACKNOWLEDGEMENTS Thanks are due to several people, without whom this work would not be appearing in its present form. I benefited greatly from an invitation of Tyler Jarvis to visit Brigham Young University. While there, I met several students working on similar material, with whom I coll ..."
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for BG. ii ACKNOWLEDGEMENTS Thanks are due to several people, without whom this work would not be appearing in its present form. I benefited greatly from an invitation of Tyler Jarvis to visit Brigham Young University. While there, I met several students working on similar material, with whom I collaborated to produce [KP+]. I enjoyed fruitful discussions with Huijin Fan, Takashi Kimura, and Ralph Kaufmann, and am grateful for the extended contact I have had with Alessandro Chiodo, whose enthusiasm and expertise were invaluable in producing this work. My studies at the University of Michigan have been generously supported by the Rackham School of Graduate Studies and the National Research Foundation of South Africa. Moral support has also been readily available, and deeply appreciated. I will cherish the wonderful friends who have left me with such happy memories of my time in Ann Arbor. Finally, I owe an inestimable debt to Yongbin Ruan. He has been remarkably generous with his time and energy, endlessly encouraging, and extremely supportive throughout.
LG/CY CORRESPONDENCE: THE STATE SPACE ISOMORPHISM
, 908
"... Abstract. We provide a degreepreserving isomorphism between the cohomology of finite quotients of Calabi–Yau hypersurfaces inside a weighted projective space and the Fan–Jarvis–Ruan–Witten state space of the associated Landau–Ginzburg singularity theory. This fulfills the physical conjectural state ..."
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Abstract. We provide a degreepreserving isomorphism between the cohomology of finite quotients of Calabi–Yau hypersurfaces inside a weighted projective space and the Fan–Jarvis–Ruan–Witten state space of the associated Landau–Ginzburg singularity theory. This fulfills the physical conjectural statement of Landau– Ginzburg/Calabi–Yau correspondence for group actions contained in the special linear group and extends it beyond. In the case of “invertible ” singularities, via a recent result of Krawitz, this yields a proof of a classical mirror symmetry conjecture for the mirror pairs constructed by Berglund, Hübsch, and Krawitz. This technique applies beyond the classical Batyrev and Borisov’s theorem which requires the ambient weighted projective space to be Gorenstein. 1.
Yefeng: LandauGinzburg/CalabiYau Correspondence of all Genera for Elliptic Orbifold P1
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Atwisted LandauGinzburg models
, 2008
"... In this paper we discuss correlation functions in certain Atwisted LandauGinzburg models. Although Btwisted LandauGinzburg models have been discussed extensively in the literature, virtually no work has been done on Atwisted theories. In particular, we study examples of LandauGinzburg models o ..."
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In this paper we discuss correlation functions in certain Atwisted LandauGinzburg models. Although Btwisted LandauGinzburg models have been discussed extensively in the literature, virtually no work has been done on Atwisted theories. In particular, we study examples of LandauGinzburg models over topologically nontrivial spaces – not just vector spaces – away from largeradius limits, so that one expects nontrivial curve corrections. By studying examples of LandauGinzburg models in the same universality class as nonlinear sigma models on nontrivial CalabiYaus, we obtain nontrivial tests of our methods as well as a physical realization of some simple examples of virtual fundamental class computations.
Gromov–Witten invariants for mirror orbifolds of simple elliptic singularities, Annales de l’institut Fourier 61
, 2011
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On the Convergence of GromovWitten Potentials and Givental’s Formula. Preprint available at 1203.4193
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