TY - JOUR

T1 - Mirror symmetry for two-parameter models (I)

AU - Candelas, Philip

AU - de la Ossa, Xenia

AU - Font, Anamaría

AU - Katz, Sheldon

AU - Morrison, David R.

N1 - Funding Information:
* Supported in part by the Robert A. Welch Foundation, NSF grants PHY-9009850, DMS-9103827 and DMS-9311386, the Swiss National Foundation, and an American Mathematical Society Centen-nial Fellowship.

PY - 1994/3/28

Y1 - 1994/3/28

N2 - We study, by means of mirror symmetry, the quantum geometry of the Kähler-class parameters of a number of Calabi-Yau manifolds that have b11 = 2. Our main interest lies in the structure of the moduli space and in the loci corresponding to singular models. This structure is considerably richer when there are two parameters than in the various one-parameter models that have been studied hitherto. We describe the intrinsic structure of the point in the (compactification of the) moduli space that corresponds to the large complex structure or classical limit. The instanton expansions are of interest owing to the fact that some of the instantons belong to families with continuous parameters. We compute the Yukawa couplings and their expansions in terms of instantons of genus zero. By making use of recent results of Bershadsky et al. we compute also the instanton numbers for instantons of genus one. For particular values of the parameters the models become birational to certain models with one parameter. The compactification divisor of the moduli space thus contains copies of the moduli spaces of one-parameter models. Our discussion proceeds via the particular models P4(1,1,2,2,2)[8] and P4(1,1,2,2,6)[12]. Another example, P4(1,1,1,6,9)[18], that is somewhat different is the subject of a companion paper.

AB - We study, by means of mirror symmetry, the quantum geometry of the Kähler-class parameters of a number of Calabi-Yau manifolds that have b11 = 2. Our main interest lies in the structure of the moduli space and in the loci corresponding to singular models. This structure is considerably richer when there are two parameters than in the various one-parameter models that have been studied hitherto. We describe the intrinsic structure of the point in the (compactification of the) moduli space that corresponds to the large complex structure or classical limit. The instanton expansions are of interest owing to the fact that some of the instantons belong to families with continuous parameters. We compute the Yukawa couplings and their expansions in terms of instantons of genus zero. By making use of recent results of Bershadsky et al. we compute also the instanton numbers for instantons of genus one. For particular values of the parameters the models become birational to certain models with one parameter. The compactification divisor of the moduli space thus contains copies of the moduli spaces of one-parameter models. Our discussion proceeds via the particular models P4(1,1,2,2,2)[8] and P4(1,1,2,2,6)[12]. Another example, P4(1,1,1,6,9)[18], that is somewhat different is the subject of a companion paper.

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U2 - 10.1016/0550-3213(94)90322-0

DO - 10.1016/0550-3213(94)90322-0

M3 - Article

AN - SCOPUS:0001165005

SN - 0550-3213

VL - 416

SP - 481

EP - 538

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 2

ER -