The Satake sextic in F-theory

DOI10.1016/j.geomphys.2017.06.010zbMath1376.14047arXiv1609.04341OpenAlexW2520295258MaRDI QIDQ2410655

Andreas Malmendier, Tanush Shaska

Publication date: 18 October 2017

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.04341

zbMATH Keywords

F-theory/heterotic string dualityJacobian elliptic fibrations on \(K3\) surfacesKummer surfaces of genus-two curves

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Modular and automorphic functions (11F03) Relationships between surfaces, higher-dimensional varieties, and physics (14J81)

Related Items

On the duality of F-theory and the CHL string in seven dimensions ⋮ On isogenies among certain abelian surfaces ⋮ Isogenous components of Jacobian surfaces ⋮ Kummer sandwiches and Greene-Plesser construction ⋮ On Kummer‐like surfaces attached to singularity and modular forms ⋮ A universal genus-two curve from Siegel modular forms ⋮ Ubiquity of non-geometry in heterotic compactifications ⋮ On Néron-Severi lattices of Jacobian elliptic \(K3\) surfaces ⋮ Genus two Siegel quasi-modular forms and Gromov-Witten theory of toric Calabi-Yau threefolds ⋮ Some remarks on the non-real roots of polynomials ⋮ Non-geometric vacua of the Spin(32)/\({\mathbb{Z}}_2\) heterotic string and little string theories ⋮ Unnamed Item ⋮ The duality between F-theory and the heterotic string in \(D=8\) with two Wilson lines ⋮ Nongeometric heterotic strings and dual F-theory with enhanced gauge groups ⋮ Isogenies of certain \(K3\) surfaces of rank 18 ⋮ The weighted moduli space of binary sextics ⋮ Computing heights on weighted projective spaces ⋮ On hyperelliptic curves of genus 3 ⋮ Six line configurations and string dualities

Cites Work

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• Lattice polarized \(K3\) surfaces and Siegel modular forms
• Explicit CM theory for level 2-structures on abelian surfaces
• Tata lectures on theta III. In collaboration with Madhav Nori and Peter Norman
• Kummer sandwich theorem of certain elliptic \(K3\) surfaces
• On metamorphosis of Kummer surfaces
• Non-simply-connected gauge groups and rational points on elliptic curves
• A universal genus-two curve from Siegel modular forms
• Correspondences between \(K3\) surfaces (with an appendix by Igor Dolgachev)
• \(K3\) surfaces, modular forms, and non-geometric heterotic compactifications
• Modular invariants for lattice polarized \(K3\) surfaces
• On compact analytic surfaces. III
• The complete classification of fibres in pencils of curves of genus two
• Elliptic fibrations on a generic Jacobian Kummer surface
• On the algebra of Siegel modular forms of genus $2$
• Computing Humbert Surfaces
• Note on a Geometric Isogeny of K3 Surfaces
• K3 Surfaces Associated with Curves of Genus Two
• Theta functions and algebraic curves with automorphisms
• Igusa modular forms and 'the simplest' Lorentzian Kac-Moody algebras
• Vector Bundles over Elliptic Fibrations
• On Siegel Modular Forms of Genus Two
• Modular Forms and Projective Invariants