Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmüller curve
From MaRDI portal
Publication:2505543
DOI10.1007/s00222-006-0510-3zbMath1111.14019arXivmath/0410262OpenAlexW2147240893MaRDI QIDQ2505543
Publication date: 26 September 2006
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0410262
Compact Riemann surfaces and uniformization (30F10) Abelian varieties of dimension (> 1) (11G10) Special algebraic curves and curves of low genus (14H45) Jacobians, Prym varieties (14H40) Teichmüller theory for Riemann surfaces (30F60) Riemann surfaces; Weierstrass points; gap sequences (14H55) Families, moduli of curves (analytic) (14H15)
Related Items
Billiards and Teichmüller curves ⋮ Splitting mixed Hodge structures over affine invariant manifolds ⋮ The equation of the Kenyon-Smillie \((2, 3, 4)\)-Teichmüller curve ⋮ From rational billiards to dynamics on moduli spaces ⋮ Schwarz triangle mappings and Teichmüller curves: The Veech-Ward-Bouw-Möller curves ⋮ Congruence Veech groups ⋮ Semisimplicity and rigidity of the Kontsevich-Zorich cocycle ⋮ Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space ⋮ Topological Veech dichotomy and tessellations of the hyperbolic plane ⋮ On the critical exponent of infinitely generated Veech groups ⋮ The boundary of an affine invariant submanifold ⋮ \(\mathrm{GL}_2\mathbb{R}\) orbit closures in hyperelliptic components of strata ⋮ Non-Existence and Finiteness Results for Teichmüller Curves in Prym Loci ⋮ The Deligne-Mumford compactification of the real multiplication locus and Teichmüller curves in genus 3 ⋮ Computing periodic points on Veech surfaces ⋮ Modular embeddings of Teichmüller curves ⋮ On the Infinite Loch Ness monster ⋮ Full-rank affine invariant submanifolds ⋮ Topological dichotomy and strict ergodicity for translation surfaces ⋮ Non-Veech surfaces in \(\mathcal H^{\mathrm{hyp}}(4)\) are generic ⋮ Linear manifolds in the moduli space of one-forms ⋮ Euler characteristics of Teichmüller curves in genus two ⋮ Teichmüller curves in genus three and just likely intersections in \(\mathbf{G}_{m}^{n}\times\mathbf{G}_{a}^{n}\) ⋮ Finiteness results for Teichmüller curves ⋮ Veech holomorphic families of Riemann surfaces, holomorphic sections, and Diophantine problems ⋮ Prym varieties and Teichmüller curves ⋮ A series of coverings of the regular \(n\)-gon ⋮ Teichmüller curves, triangle groups, and Lyapunov exponents ⋮ Teichmüller curves in genus two: Torsion divisors and ratios of sines ⋮ Book Review: Twisted Teichmüller curves ⋮ The conformal geometry of billiards ⋮ Existence of closed geodesics through a regular point on translation surfaces ⋮ Veech surfaces and their periodic points ⋮ Marked points on translation surfaces ⋮ Teichm\"uller dynamics in the eyes of an algebraic geometer ⋮ Geometry and dynamics on Riemann and \(K3\) surfaces ⋮ Periodic points on the regular and double \(n\)-gon surfaces ⋮ Hodge-Teichmüller planes and finiteness results for Teichmüller curves ⋮ Platonic Solids and High Genus Covers of Lattice Surfaces
Cites Work
- Unnamed Item
- Courbes sur une variété abélienne et points de torsion
- Torsion points on curves and p-adic abelian integrals
- Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
- Hodge theory with degenerating coefficients: \(L_2\) cohomology in the Poincaré metric
- On a class of geodesics in Teichmüller space
- Affine mappings of translation surfaces: Geometry and arithmetic
- Finiteness of Mordell-Weil groups of Kuga fiber spaces of abelian varieties
- Teichmüller curves in genus two: Torsion divisors and ratios of sines
- Teichmüller curves in genus two: Discriminant and spin
- Variations of Hodge structures of a Teichmüller curve
- Planar structures and billiards in rational polygons: the Veech alternative
- Billiards and Teichmüller curves on Hilbert modular surfaces
- Affine diffeomorphisms of translation surfaces: Periodic points, Fuchsian groups, and arithmeticity
- Examples of torsion points on genus two curves
- Teichmüller curves in genus two: The decagon and beyond
- On a question of B. Mazur
- Invariants of translation surfaces