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Original Articles

Effective Reconstruction of Generic Genus 5 Curves from their Theta Hyperplanes

References

  • Aronhold, S. (1864). Über den gegenseitigen Zusamemmenhang der 28 Doppeltangenten einer allgemeiner Curve 4ten Grades, Monatberichter der Akademie der Wissenschaften zu Berlin, 499–523.
  • Arbarello, E., Cornalba, M., Griffiths, P. A., Harris, J. (1985). Geometry of Algebraic Curves, Vol. I. Grundlehren der Mathematischen Wisse nschaften, 267. New York, NY: Springer-Verlag.
  • Breiding, P., Sturmfels, B., Timme, S. (2020). 3264 conics in a second. Not. Am. Math. Soc. 67: 30–37
  • Celik, T. O., Kulkarni, A., Ren, Y., Namin, M. S. (2019). Tritangents and their space sextics. J. Algebra. 538: 290–311. doi:10.1016/j.jalgebra.2019.07.037
  • Caporaso, L., Sernesi, E. Recovering plane curves from their bitangents. J. Algebraic Geom. 12: 225–244. doi:10.1090/S1056-3911-02-00307-7
  • Caporaso, L., Sernesi, E. (2003). Characterizing curves by their odd theta-characteristics. J. Reine Angew. Math. 562: 101–135.
  • Coble, A. (1961). Algebraic Geometry and Theta Functions, revised printing. Providence, RI: American Mathematical Society Colloquium Publications.
  • Dolgachev, I. (2012). Classical Algebraic Geometry: A Modern View. Cambridge, UK: Cambridge University Press.
  • Dolgachev, I., Farb, B., Looijenga, E. Geometry of the Wiman Pencil, I: Algebro-Geometric Aspects. Eur. J. Math. 4: 879–930. doi:10.1007/s40879-018-0231-3
  • Edge, W. (1969). Three plane sextics and their automorphisms. Can. J. Math. 21: 1263–1278. doi:10.4153/CJM-1969-139-6
  • Grushevsky, S., Salvati-Mani, R. (2004). On the gradient of odd theta functions. J. Reine Angew. Math. 573: 45–59. doi:10.1515/crll.2004.063
  • Grushevsky, S., Salvati-Mani, R. (2006). Theta functions of arbitrary order and their derivatives. J. Reine Angew. Math. 590: 31–43.
  • Humbert, G. (1894). Sur un complex remarguable de coniques et sur la surface du troisiéme ordre. J. Ecole Polytechnique. 64: 123–149.
  • Hauenstein, J. D., Sottile, F. (2012). alphaCertified: Certifying Solutions to Polynomial Systems. ACM Trans. Math. Softw. 38: 28. doi:10.1145/2331130.2331136
  • Lehavi, D. (2005). Any smooth plane quartic can be reconstructed from its bitangents. Isr. J. Math. 146: 371–379. doi:10.1007/BF02773542
  • Lehavi, D. (2015). Effective reconstruction of generic genus 4 curves from their theta hyperplanes. Int. Math. Res. Not. 2: 9472–9485. doi:10.1093/imrn/rnu235
  • Macbeath, A. (1965). On a curve of genus 7. Proc. London Math. Soc. 15: 527–542. doi:10.1112/plms/s3-15.1.527
  • Odlyzko, A. M., Schönhage, A. (1988). Fast algorithms for multiple evaluations of the Riemann zeta function. Trans. Am. Math. Soc. 309: 797–809. doi:10.1090/S0002-9947-1988-0961614-2
  • Varley, R. (1986). Weddle’s surfaces, Humbert’s curves, and a certain 4-dimensional abelian variety. Amer. J. Math. 108: 931–952.
  • Wiman, A. (1895). Über die algebraischen Curven von den Geschlechtern p = 4, 5 und 6, welche eindeutige Transformationen in sich besitsen, Svenska Vet.-Akad Handlingar Bihang till Handlingar 21 afd 1, No. 3.

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