Gauss-Manin connection in disguise: Calabi-Yau threefolds

DOI10.1007/s00220-016-2640-9zbMath1348.14103arXiv1410.1889OpenAlexW2964219461MaRDI QIDQ2630726

Murad Alim, Emanuel Scheidegger, Hossein Movasati, Shing Tung Yau

Publication date: 21 July 2016

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.1889

zbMATH Keywords

mirror symmetryquasi-modular formsholomorphic anomaly equationstopological string partition functionmirror quinticGrothendieck's de Rham cohomologyspecial geometry of deformation spaces

Mathematics Subject Classification ID

Calabi-Yau manifolds (algebro-geometric aspects) (14J32) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Mirror symmetry (algebro-geometric aspects) (14J33)

Related Items

Algebraic structure of \(t\,t{*}\) equations for Calabi-Yau sigma models, Metric in the moduli of SU(2) monopoles from spectral curves and Gauss-Manin connection in disguise, Manifold ways to Darboux-Halphen system, Gauss-Manin connection in disguise: genus two curves, Gauss-Manin connection in disguise: Dwork family

Cites Work

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• Global properties of topological string amplitudes and orbifold invariants
• Special polynomial rings, quasi modular forms and duality of topological strings
• Eisenstein type series for Calabi-Yau varieties
• Holomorphic anomalies in topological field theories
• On Ramanujan relations between Eisenstein series
• Special geometry
• Moduli space of Calabi-Yau manifolds
• A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory.
• Modular-type functions attached to mirror quintic Calabi-Yau varieties
• On elliptic modular foliations
• Topological sigma models
• Mirror principle. I
• Hodge cycles, motives, and Shimura varieties
• Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
• Local and global theory of the moduli of polarized Calabi-Yau manifolds
• Quasi-modular forms attached to elliptic curves. I
• Darboux-Halphen-Ramanujan vector field on a moduli of Calabi-Yau manifolds
• On the equations of Halphen and \(\mathrm{SL}_{2}(\mathbb C)\)-actions
• On the differentiation of De Rham cohomology classes with respect to parameters
• Quasi-modular Forms Attached to Hodge Structures
• The reduced genus $1$ Gromov-Witten invariants of Calabi-Yau hypersurfaces
• BCOV ring and holomorphic anomaly equation
• Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions
• Homological Algebra of Mirror Symmetry
• Lectures on Mirror Symmetry and Topological String Theory
• Equivariant Gromov - Witten Invariants
• On the De Rham cohomology of algebraic varieties