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The monomialdivisor mirror map
 Internat. Math. Research Notices
, 1993
"... For each family of CalabiYau hypersurfaces in toric varieties, Batyrev has proposed a possible mirror partner (which is also a family of CalabiYau hypersurfaces). We explain a natural construction of the isomorphism between certain Hodge groups of these hypersurfaces, as predicted by mirror symmet ..."
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Cited by 25 (2 self)
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symmetry, which we call the monomialdivisor mirror map. We indicate how this map can be interpreted as the differential of the expected mirror isomorphism between the moduli spaces of the two CalabiYau manifolds. We formulate a very precise conjecture about the form of that mirror isomorphism, which when
The MonomialDivisor Mirror Map for
, 1994
"... We present the new explicit geometrical knowledge of the LandauGinzburg orbifolds, when a typical type of superpotential is considered. Relying on toric geometry, we show the onetoone correspondence between some of the (a, c) states with U(1) charges (−1, 1) and the (1, 1) forms coming from blowi ..."
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blowingup processes. Consequently, we find the monomialdivisor mirror map for LandauGinzburg orbifolds. The possibility of the application of the models of other types is briefly discussed. N = 2 superconformal field theory has attracted the attention in the context of string compactification [1]. Due
Seidel’s Mirror Map for the Torus
"... Abstract. Using only the Fukaya category and the monodromy around large complex structure, we reconstruct the mirror map in the case of a symplectic torus. This realizes an idea described by Paul Seidel. ..."
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Cited by 6 (1 self)
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Abstract. Using only the Fukaya category and the monodromy around large complex structure, we reconstruct the mirror map in the case of a symplectic torus. This realizes an idea described by Paul Seidel.
Mirror symmetry, mirror map and applications to complete . . .
 EXPERIMENTAL NUCLEAR PHYSICS B
, 1995
"... ..."
Frobenius transformation, mirror map and instanton
 B 660 (2008), 422–427, Preprint hepth/0606151
"... We show that one can express Frobenius transformation on middledimensional padic cohomology of CalabiYau threefold in terms of mirror map and instanton numbers. We express the mirror map in terms of Frobenius transformation on padic cohomology. We discuss a padic interpretation of the conjectur ..."
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Cited by 7 (4 self)
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We show that one can express Frobenius transformation on middledimensional padic cohomology of CalabiYau threefold in terms of mirror map and instanton numbers. We express the mirror map in terms of Frobenius transformation on padic cohomology. We discuss a padic interpretation
ON GENERALIZED HYPERGEOMETRIC EQUATIONS AND MIRROR MAPS
"... Abstract. This paper deals with generalized hypergeometric differential equations of order n ≥ 3 having maximal unipotent monodromy at 0. We show that, among these equations, those leading to mirror maps with integral Taylor coefficients at 0 (up to simple rescaling) have special parameters, namely ..."
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Cited by 3 (0 self)
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Abstract. This paper deals with generalized hypergeometric differential equations of order n ≥ 3 having maximal unipotent monodromy at 0. We show that, among these equations, those leading to mirror maps with integral Taylor coefficients at 0 (up to simple rescaling) have special parameters, namely
PicardFuchs Equations and Mirror Maps For Hypersurfaces
 IN ESSAYS ON MIRROR MANIFOLDS, ED. S.T.YAU, INTERNATIONAL PRESS
, 1992
"... We describe a strategy for computing Yukawa couplings and the mirror map, based on the PicardFuchs equation. (Our strategy is a variant of the method used by Candelas, de la Ossa, Green, and Parkes [5] in the case of quintic hypersurfaces.) We then explain a technique of Griffiths [14] which can ..."
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Cited by 102 (5 self)
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We describe a strategy for computing Yukawa couplings and the mirror map, based on the PicardFuchs equation. (Our strategy is a variant of the method used by Candelas, de la Ossa, Green, and Parkes [5] in the case of quintic hypersurfaces.) We then explain a technique of Griffiths [14] which can
The mirror map for invertible LG models
, 1994
"... Calculating the (a,c) ring of the maximal phase orbifold for ‘invertible ’ Landau–Ginzburg models, we show that the Berglund–Hübsch construction works for all potentials of the relevant type. The map that sends a monomial in the original model to a twisted state in the orbifold representation of the ..."
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Cited by 9 (1 self)
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of the mirror is constructed explicitly. Via this map, the OP selection rules of the chiral ring exactly correspond to the twist selection rules for the orbifold. This shows that we indeed arrive at the correct point in moduli space, and that the mirror map can be extended to arbitrary orbifolds, including non
On the integrality of the Taylor coefficients of mirror maps
, 2007
"... Abstract. We show that the Taylor coefficients of the series q(z) = z exp(G(z)/F(z)) are integers, where F(z) and G(z) + log(z)F(z) are specific solutions of certain hypergeometric differential equations with maximal unipotent monodromy at z = 0. We also address the question of finding the largest ..."
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Cited by 20 (5 self)
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integer u such that the Taylor coefficients of (z−1q(z)) 1/u are still integers. As consequences, we are able to prove numerous integrality results for the Taylor coefficients of mirror maps of Calabi–Yau complete intersections in weighted projective spaces, which improve and refine previous results
Results 1  10
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233,666