Teichmüller curves in genus two: Discriminant and spin
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Publication:2574909
DOI10.1007/s00208-005-0666-yzbMath1086.14024OpenAlexW1995948987MaRDI QIDQ2574909
Publication date: 5 December 2005
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00208-005-0666-y
Families, moduli of curves (algebraic) (14H10) Special algebraic curves and curves of low genus (14H45) Modular and Shimura varieties (14G35) Teichmüller theory for Riemann surfaces (30F60) Riemann surfaces; Weierstrass points; gap sequences (14H55)
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Cites Work
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- On the intersection of modular correspondences
- Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
- The billiard in a regular polygon
- Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
- Billiards in rectangles with barriers
- Connected components of the moduli spaces of Abelian differentials with prescribed singularities
- Billiards on rational-angled triangles
- Affine mappings of translation surfaces: Geometry and arithmetic
- Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singu\-larities
- Teichmüller geodesics of infinite complexity.
- Endomorphism rings of abelian surfaces and projective models of their moduli spaces
- Teichmüller curves in genus two: Torsion divisors and ratios of sines
- Über eine zahlentheoretische Funktion von Jacobsthal
- Spin Structures and Quadratic forms on Surfaces
- Calculation of Fuchsian groups associated to billiards in a rational triangle
- Planar structures and billiards in rational polygons: the Veech alternative
- Billiards and Teichmüller curves on Hilbert modular surfaces
- Veech surfaces and complete periodicity in genus two
- On the Integers Relatively Prime to $n$ and a Number-Theoretic Function Considered by Jacobsthal.
- Riemann surfaces and spin structures
- Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
- On triangular billiards