Mirror Symmetry for Two Parameter Models -- II by Candelas, P, Font, A, Katz, S, Morrison, DR

“…We describe in detail the space of the two K\"ahler parameters of the Calabi--Yau manifold $\P_4^{(1,1,1,6,9)}[18]$ by exploiting mirror symmetry. …”

The moduli space of complex Lagrangian submanifolds by Hitchin, N

“…Following an earlier paper on the differential-geometric structure of the moduli space of special Lagrangian submanifolds in a Calabi-Yau manifold, we follow an analogous approach for compact complex Lagrangian submanifolds of a (K\"ahlerian) complex symplectic manifold. …”

Scanning the Landscape of Flux Compactifications: Vacuum Structure and Soft Supersymmetry Breaking by AbdusSalam, S, Conlon, J, Quevedo, F, Suruliz, K

“…We scan the landscape of flux compactifications for the Calabi-Yau manifold $\mathbb{P}^4_{[1,1,1,6,9]}$ with two K\" ahler moduli by varying the value of the flux superpotential $W_0$ over a large range of values. …”

Symmetries of Calabi-Yau prepotentials with isomorphic flops by Lukas, A, Ruehle, F

“…For some cases, these functions can be expressed in terms of theta functions whose appearance can be linked to an elliptic fibration structure of the Calabi-Yau manifold.</p>…”

The Atiyah class and complex structure stabilization in heterotic Calabi-Yau compactifications by Anderson, L, Gray, J, Lukas, A, Ovrut, B

“…Holomorphic gauge fields in N = 1 supersymmetric heterotic compactifications can constrain the complex structure moduli of a Calabi-Yau manifold. In this paper, the tools necessary to use holomorphic bundles as a mechanism for moduli stabilization are systematically developed. …”

Matter field Kahler metric in heterotic string theory from localisation by Blesneag, Ş, Buchbinder, E, Constantin, A, Lukas, A, Palti, E

“…In a final step, we show how this local result can be expressed in terms of the global moduli of the Calabi-Yau manifold. The method is illustrated for the family of Calabi-Yau hypersurfaces embedded in ℙ1× ℙ3and we obtain an explicit result for the matter field Kähler metric in this case.…”

The exceptional holonomy groups and calibrated geometry by Joyce, D

“…There are also more complicated constructions which begin with a Calabi-Yau manifold or orbifold. Part II discusses the calibrated submanifolds of G2 and Spin(7)-manifolds: associative 3-folds and coassociative 4-folds for G2, and Cayley 4-folds for Spin(7). …”

Matter field Kähler metric in heterotic string theory from localisation by Blesneag, S, Buchbinder, E, Constantin, A, Lukas, A, Palti, E

“…In a final step, we show how this local result can be expressed in terms of the global moduli of the Calabi-Yau manifold. The method is illustrated for the family of Calabi-Yau hypersurfaces embedded in P1 × P3 and we obtain an explicit result for the matter field Kähler metric in this case.…”

The origin of Calabi-Yau crystals in BPS states counting by Jiakang Bao, Rak-Kyeong Seong, Masahito Yamazaki

“…Abstract We study the counting problem of BPS D-branes wrapping holomorphic cycles of a general toric Calabi-Yau manifold. We evaluate the Jeffrey-Kirwan residues for the flavoured Witten index for the supersymmetric quiver quantum mechanics on the worldvolume of the D-branes, and find that BPS degeneracies are described by a statistical mechanical model of crystal melting. …”
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Symmetric fluxes and small tadpoles by Thibaut Coudarchet, Fernando Marchesano, David Prieto, Mikel A. Urkiola

“…We illustrate this approach in a Calabi-Yau manifold with 51 complex structure moduli, where several reduction schemes can be implemented in order to explicitly solve the vacuum equations for that sector. …”
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YUKAWA COUPLINGS BETWEEN (2,1)-FORMS by Candelas, P

“…The generalization of this process is presented for a general Calabi-Yau manifold. © 1988.…”

Tuned and non-Higgsable U(1)s in F-theory by Wang, Y

“…In particular, we show that the elliptic Calabi-Yau manifold over such a base has a small number of complex structure moduli. …”

On the moduli space curvature at infinity by Fernando Marchesano, Luca Melotti, Lorenzo Paoloni

“…Abstract We analyse the scalar curvature of the vector multiplet moduli space M X VM $$ {\mathcal{M}}_X^{\textrm{VM}} $$ of type IIA string theory compactified on a Calabi-Yau manifold X. While the volume of M X VM $$ {\mathcal{M}}_X^{\textrm{VM}} $$ is known to be finite, cases have been found where the scalar curvature diverges positively along trajectories of infinite distance. …”
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Cutting the traintracks: Cauchy, Schubert and Calabi-Yau by Qu Cao, Song He, Yichao Tang

“…For L-loop full traintracks, we compute their leading singularities as integrals of (L−1)-forms, which proves that the rigidity is L−1 as expected; the form is given by an inverse square root of an irreducible polynomial quartic with respect to each variable, which characterizes an (L−1)-dim Calabi-Yau manifold (elliptic curve, K3 surface, etc.) for any L. …”
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Compact G2 holonomy spaces from SU(3) structures by S. Andriolo, G. Shiu, H. Triendl, T. Van Riet, G. Venken, G. Zoccarato

“…The backreaction of these fluxes deforms the Calabi-Yau manifold into a specific class of SU(3)-structure manifolds. …”
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Smearing and unsmearing KKLT AdS vacua by Mariana Graña, Nicolas Kovensky, Dimitrios Toulikas

“…We show that supersymmetry requires a (conformal) Calabi-Yau manifold and imaginary self-dual three-form fluxes with an additional (0,3) component. …”
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Tuned and non-Higgsable U(1)s in F-theory by Wang, Yinan

“…In particular, we show that the elliptic Calabi-Yau manifold over such a base has a small number of complex structure moduli. …”
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Calibrations and minimal Lagrangian submanifolds by Goldstein, Edward, 1977-

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General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure by Cvetič, Mirjam, Klevers, Denis, Piragua, Hernan, Taylor IV, Washington

“…We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. …”
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Investigations in Calabi-Yau modularity and mirror symmetry by McGovern, J

“…<p>This thesis lays out a number of different projects, linked by the common thread of Calabi-Yau manifolds.</p> <p>We produce tables of instanton numbers for various multiparameter Calabi-Yau manifolds. …”