This is a preview of subscription content, log in via an institution to check access.
References
Atiyah, M.F.: Riemann surfaces and spin structures. Ann. scient. Éc. Norm. Sup. 4, 47–62 (1971)
Birkenhake, C., Lange, H.: Complex Abelian Varieties. Springer-Verlag, 1992
Calta, K.: Veech surfaces and complete periodicity in genus 2. J. Amer. Math. Soc. 17, 871–908 (2004)
Erdös, P.: On the integers relatively prime to n and on a number-theoretic function considered by Jacobsthal. Math. Scand. 10, 163–170 (1962)
Eskin A., Masur H., Schmoll, M.: Billiards in rectangles with barriers. Duke Math. J. 118, 427–463 (2003)
Eskin A., Okounkov, A.: Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials. Invent. math. 145, 59–103 (2001)
van der Geer, G.: Hilbert Modular Surfaces. Springer, Berlin Heidelberg, 1987
Gross, B.H., Keating, K.: On the intersection of modular correspondences. Invent. math. 112, 225–245 (1993)
Gutkin, E., Judge, C.: Affine mappings of translation surfaces: geometry and arithmetic. Duke Math. J. 103, 191–213 (2000)
Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers. Oxford University Press, 1979
Hirzebruch, F., Zagier, D.: Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus. Invent. math. 36, 57–113 (1976)
Hubert, P., Lelièvre, S.: Square-tiled surfaces in
Preprint, 2004Jacobsthal, E.: Über Sequenzen ganzer Zahlen, von denen keine zu n teilerfremd ist. I, II, III. Norke Vid. Selsk. Forh. Trondheim 33, 117–124, 125–131, 132–139 (1961)
Johnson, D.: Spin structures and quadratic forms on surfaces. J. London Math. Soc. 22, 365–373 (1980)
Kanold, H.-J.: Über eine zahlentheoretische Funktion von Jacobsthal. Math. Ann. 170, 314–326 (1967)
Kenyon, R., Smillie, J.: Billiards on rational-angled triangles. Comment. Math. Helv. 75, 65–108 (2000)
Knapp, A.W.: Elliptic Curves. Princeton University Press, 1992
Kontsevich, M., Zorich, A.: Connected components of the moduli spaces of Abelian differentials with prescribed singularities. Invent. math. 153, 631–678
Lang, S.: Elliptic Functions. Springer-Verlag, 1987
Lanneau, E.: Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities. Comment. Math. Helv. 79, 471–501 (2004)
McMullen, C.: Billiards and Teichmüller curves on Hilbert modular surfaces. J. Amer. Math. Soc. 16, 857–885 (2003)
McMullen, C.: Teichmüller geodesics of infinite complexity. Acta Math. 191, 191–223 (2003)
McMullen, C.: Dynamics of SL2(ℝ) over moduli space in genus two. Preprint, 10/2003
McMullen, C.: Teichmüller curves in genus two: Torsion divisors and ratios of sines. Preprint, 9/2004
Puchta, J.-C.: On triangular billiards. Comment. Math. Helv. 76, 501–505 (2001)
Runge, B.: Endomorphism rings of abelian surfaces and projective models of their moduli spaces. Tôhoku Math. J. 51, 283–303 (1999)
Serre, J.P.: A Course in Arithmetic. Springer, Berlin Heidelberg, 1973
Stevens, H.: On Jacobsthal’s g(n)-function. Math. Ann. 226, 95–97 (1977)
Veech, W.: Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards. Invent. math. 97, 553–583 (1989)
Veech, W.: The billiard in a regular polygon. Geom. Funct. Anal. 2, 341–379 (1992)
Vorobets, Ya.B.: Plane structures and billiards in rational polygons: the Veech alternative. Russian Math. Surveys 51, 779–817 (1996)
Ward, C.C.: Calculation of Fuchsian groups associated to billiards in a rational triangle. Ergod. Th. & Dynam. Sys. 18, 1019–1042 (1998)
Preprint, 2004Author information
Authors and Affiliations
Additional information
Research partially supported by the NSF.
Rights and permissions
About this article
Cite this article
McMullen, C. Teichmüller curves in genus two: Discriminant and spin. Math. Ann. 333, 87–130 (2005). https://doi.org/10.1007/s00208-005-0666-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00208-005-0666-y