Modular embeddings of Teichmüller curves

DOI10.1112/S0010437X16007636zbMath1386.14118arXiv1503.05690OpenAlexW3102033094MaRDI QIDQ5360247

Don Zagier, Martin Möller

Publication date: 28 September 2017

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.05690

zbMATH Keywords

modular formstheta functionsHilbert modular surfacesTeichmüller curves

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) Theta series; Weil representation; theta correspondences (11F27) Arithmetic aspects of modular and Shimura varieties (11G18) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (11)

Billiards and Teichmüller curves ⋮ Higher pullbacks of modular forms on orthogonal groups ⋮ The arithmetic and topology of differential equations ⋮ Splitting mixed Hodge structures over affine invariant manifolds ⋮ Ramanujan systems of Rankin-Cohen type and hyperbolic triangles ⋮ Cones of Heegner divisors ⋮ The Galois Action and a Spin Invariant for Prym-Teichmüller Curves in Genus 3 ⋮ Moduli spaces of isoperiodic forms on Riemann surfaces ⋮ Euler characteristics of gothic Teichmüller curves ⋮ Non-congruence of homology Veech groups in genus two ⋮ ORBIFOLD POINTS ON PRYM–TEICHMÜLLER CURVES IN GENUS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Deligne-Mumford compactification of the real multiplication locus and Teichmüller curves in genus 3
• Moduli spaces of isoperiodic forms on Riemann surfaces
• Fundamental domains and generators for lattice Veech groups
• Kobayashi geodesics in \(\mathcal A_g\)
• Der Überlagerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen
• Teichmüller curves, triangle groups, and Lyapunov exponents
• The 1-2-3 of modular forms. Lectures at a summer school in Nordfjordeid, Norway, June 2004
• Symmetrische Hilbertsche Modulformen und Modulfunktionen zu \(\mathbb Q(\sqrt{17})\)
• Eine arithmetische Eigenschaft automorpher Formen zu gewissen nicht- arithmetischen Gruppen
• Modular forms associated to real quadratic fields
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• On the values at negative integers of the zeta-function of a real quadratic field
• Hilbert modular surfaces
• Mixed automorphic forms, torus bundles, and Jacobi forms
• Twisted Teichmüller curves
• Orbifold points on Teichmüller curves and Jacobians with complex multiplication
• Euler characteristics of Teichmüller curves in genus two
• Prym varieties and Teichmüller curves
• Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmüller curve
• Teichmüller curves in genus two: Torsion divisors and ratios of sines
• Harmonic analysis and theta-functions
• Teichmüller curves in genus two: Discriminant and spin
• Prym covers, theta functions and Kobayashi curves in Hilbert modular surfaces
• Introduction to Toric Varieties. (AM-131)
• Symmetric Fuchsian Quadrilateral Groups and Modular Embeddings
• Modular embeddings for some non-arithmetic Fuchsian groups
• Variations of Hodge structures of a Teichmüller curve
• Differential equations associated with nonarithmetic Fuchsian groups
• Foliations of Hilbert modular surfaces
• Billiards and Teichmüller curves on Hilbert modular surfaces
• Semi-Arithmetic Fuchsian Groups and Modular Embeddings
• Algebraic Models and Arithmetic Geometry of Teichmüller Curves in Genus Two
• Veech surfaces and complete periodicity in genus two
• The Modular Groups of Hilbert and Siegel
• On the uniform equidistribution of long closed horocycles

This page was built for publication: Modular embeddings of Teichmüller curves