Modularity of Calabi–Yau Varieties: 2011 and Beyond

DOI10.1007/978-1-4614-6403-7_4zbMath1302.14005arXiv1212.4308OpenAlexW1542623579MaRDI QIDQ2926112

Noriko Yui

Publication date: 30 October 2014

Published in: Fields Institute Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.4308

zbMATH Keywords

elliptic curvesmirror symmetryCalabi-Yau threefolds\(K3\) surfacesGalois representationsPicard-Fuchs differential equationsmirror mapsautomorphic inductionsCM type Calabi-Yau varietiesFamilies of Calabi-Yau varietiesgeometry and arithmetic of moduli spacesHilbert and Siegel modular formsmodular (cusp) forms

Mathematics Subject Classification ID

History of mathematics in the 21st century (01A61) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Galois representations (11F80) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) History of algebraic geometry (14-03) Moduli, classification: analytic theory; relations with modular forms (14J15) Mirror symmetry (algebro-geometric aspects) (14J33) Arithmetic mirror symmetry (11G42)

Related Items (9)

The arithmetic and topology of differential equations ⋮ Newforms with rational coefficients ⋮ The Root Lattice $$A_{2}$$ in the Construction of Substitution Tilings and Singular Hypersurfaces ⋮ \(K3\) mirror symmetry, Legendre family and Deligne's conjecture for the Fermat quartic ⋮ Singular and Calabi-Yau varieties linked with billiard trajectories and diffusion operators ⋮ CY-operators and $L$-functions ⋮ Computing special \(L\)-values of certain modular forms with complex multiplication ⋮ Periods of rigid double octic Calabi–Yau threefolds ⋮ Voisin's conjecture for zero-cycles on Calabi-Yau varieties and their mirrors

Cites Work

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• Modular forms and \(K3\) surfaces
• On the modularity of rigid Calabi-Yau threefolds: epilogue
• Automorphy of Calabi-Yau threefolds of Borcea-Voisin type over \(\mathbb{Q}\)
• Geometry and arithmetic of Maschke's Calabi-Yau three-fold
• Modularity of Maschke's octic and Calabi-Yau threefold
• Counting hyperelliptic curves on an abelian surface with quasi-modular forms
• Rigid Calabi-Yau threefolds over \(\mathbb Q\) are modular
• The Berglund-Hübsch-Chiodo-Ruan mirror symmetry for \(K3\) surfaces
• Automorphisms of even lattices that arise in connection with automorphisms of algebraic K3-surfaces
• Hypersurface simple K3 singularities
• Superconformal algebras and mock theta functions. II: Rademacher expansion for \(K3\) surface
• On the integrality of the Taylor coefficients of mirror maps. II
• On the integrality of the Taylor coefficients of mirror maps
• The modularity of \(K3\) surfaces with non-symplectic group actions
• The 1-2-3 of modular forms. Lectures at a summer school in Nordfjordeid, Norway, June 2004
• Modularity of some non-rigid double octic Calabi-Yau threefolds
• Cyclic coverings, Calabi-Yau manifolds and complex multiplication
• Serre's modularity conjecture. II
• Modularity of 2-adic Barsotti-Tate representations
• Hodge cycles, motives, and Shimura varieties
• Automorphisms of algebraic K3 surfaces which act trivially on Picard groups
• On Shioda-Inose structures of one-parameter families of \(K3\) surfaces
• Mirror symmetry for lattice polarized \(K3\) surfaces
• On K3 surfaces with large Picard number
• On the geometry and arithmetic of some Siegel modular threefolds
• Motivic orthogonal two-dimensional representations of \(\text{Gal}(\overline\mathbb{Q}/\mathbb{Q})\)
• Arithmetic properties of mirror map and quantum coupling
• New families of Calabi-Yau threefolds without maximal unipotent monodromy
• Modularity of the Consani-Scholten quintic. With an appendix by José Burgos Gil and Ariel Pacetti
• Period- and mirror-maps for the quartic \(K3\)
• Differential equations satisfied by modular forms and \(K3\) surfaces
• Modular Calabi-Yau threefolds
• Two Lectures on the Arithmetic of K3 Surfaces
• Quadratic Twists of Rigid Calabi–Yau Threefolds Over ℚ
• Rationality of the moduli spaces of 2-elementary 𝐾3 surfaces
• A Modular Quintic Calabi-Yau Threefold of Level 55
• Hilbert Modular Forms and Their Applications
• Siegel Modular Forms and Their Applications
• Some Siegel threefolds with a Calabi-Yau model
• On modularity of rigid and nonrigid Calabi-Yau varieties associated to the Root Lattice A₄
• On the Modularity of Three Calabi–Yau Threefolds With Bad Reduction at 11
• Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
• Update on Modular Non-Rigid Calabi-Yau Threefolds
• Superconformal algebras and mock theta functions
• INTEGRAL SYMMETRIC BILINEAR FORMS AND SOME OF THEIR APPLICATIONS
• Hodge groups of K3 surfaces.
• ARITHMETIC ON A QUINTIC THREEFOLD
• Period map of a certain K3 family with an 𝔖5-action
• Mirror maps, modular relations and hypergeometric series. II

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