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MAGMA Computational Algebra System

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Algebraic Geometry

Curves

14Hxx

[1] Kontogeorgis Aristides and Victor Rotger. On abelian automorphism groups of Mumford curves and applications to Shimura curves. arXiv:math.AG/0604099, 16 pages, 2006.
[2] S. Arita, S. Miura, and T. Sekiguchi. An addition algorithm on the Jacobian varieties of curves. J. Ramanujan Math. Soc., 19(4):235–251, 2004.
[3] Philip Boalch. Higher genus icosahedral Painlevé curves. Funk. Ekvac. (Kobe),, 50:19–32, 2007.
[4] Irene I. Bouw and Stefan Wewers. Indigenous bundles with nilpotent p-curvature. Int. Math. Res. Not., Art. ID 89254, 37 pages, 2006.
[5] Nils Bruin. The arithmetic of Prym varieties in genus 3. arXiv:math.NT/0408069 v1, 20 pages, 2004.
[6] E. Bujalance, M. D. E. Conder, J. M. Gamboa, G. Gromadzki, and M. Izquierdo. Double coverings of Klein surfaces by a given Riemann surface. J. Pure Appl. Algebra, 169(2-3):137–151, 2002.
[7] Emilio Bujalance, F. J. Cirre, and Marston Conder. On extendability of group actions on compact Riemann surfaces. Trans. Amer. Math. Soc., 355(4):1537–1557 (electronic), 2003.
[8] John Cremona, Tom Fisher, Cathy O'Neil, Denis Simon, and Michael Stoll. Explicit n-descent on elliptic curves II: Geometry. arXiv:math.NT/0611606, 24 pages, 2006.
[9] Laurent Ducrohet. The action of the Frobenius map on rank 2 vector bundles over genus 2 curves in small characteristics. arXiv:math.AG/0512597, 50 pages, 2005.
[10] Tom Fisher. Genus one curves defined by Pfaffians. 24 pages, 2004.
[11] Tom Fisher. Testing equivalence of ternary cubics. In Algorithmic Number Theory (Berlin, 2006), volume 4076 of Lecture Notes in Comput. Sci., pages 333–345. Springer, Berlin, 2006.
[12] P. Gaudry, F. Hess, and N. P. Smart. Constructive and destructive facets of Weil descent on elliptic curves. J. Cryptology, 15(1):19–46, 2002.
[13] P. Gaudry, T. Houtmann, D. Kohel, C. Ritzenthaler, and A. Weng. The p-adic CM-method for genus 2. arXiv:math.NT/0503148 v1, 24 pages, 2005.
[14] P. Gaudry and É. Schost. On the invariants of the quotients of the Jacobian of a curve of genus 2. In Applied Algebra, Algebraic Algorithms and Error-correcting Codes (Melbourne, 2001), volume 2227 of Lecture Notes in Comput. Sci., pages 373–386. Springer, Berlin, 2001.
[15] Martine Girard. The group of Weierstrass points of a plane quartic with at least eight hyperflexes. Math. Comp., 75(255):1561–1583 (electronic), 2006.
[16] Martine Girard and David R. Kohel. Classification of genus 3 curves in special strata of the moduli space. In Algorithmic Number Theory (Berlin, 2006), volume 4076 of Lecture Notes in Comput. Sci., pages 346–360. Springer, Berlin, 2006.
[17] Edray Herber Goins and Davin Maddox. Heron triangles via elliptic curves. Rocky Mountain J. Math., 36(5):1511–1526, 2006.
[18] V. Gritsenko, K. Hulek, and G. K. Sankaran. The Kodaira dimension of the moduli of K3 surfaces. arXiv:math/0607339, 47 pages, 2006.
[19] Jordi Guàrdia. Jacobian nullwerte, periods and symmetric equations for hyperelliptic curves. Annales de l'Institut Fourier, To appear, 11 pages, 2006.
[20] F. Hess. Computing Riemann-Roch spaces in algebraic function fields and related topics. J. Symbolic Comput., 33(4):425–445, 2002.
[21] Florian Hess. An algorithm for computing Weierstrass points. In Algorithmic Number Theory (Sydney, 2002), volume 2369 of Lecture Notes in Comput. Sci., pages 357–371. Springer, Berlin, 2002.
[22] Hendrik Hubrechts. Quasi-quadratic elliptic curve point counting using rigid cohomology. arXiv:math/0701850, 14 pages, 2007.
[23] D. Lehavi and C. Ritzenthaler. Formulas for the arithmetic geometric mean of curves of genus 3. arXiv:math.AG/0403182, 26 pages, 2005.
[24] Claus Lehr and Michel Matignon. Wild monodromy and automorphisms of curves. Duke Math. J, To appear, 15 pages, 2006.
[25] Adam Logan and Ronald van Luij. Nontrivial elements of Sha explained through K3 surfaces. arXiv:0706.0541, 37 pages, 2007.
[26] Francesco Polizzi. Standard isotrivial fibrations with pg = q = 1. arXiv:math/0703066, 30 pages, 2007.
[27] Jasper Scholten and Hui June Zhu. Families of supersingular curves in characteristic 2. Math. Res. Lett., 9(5-6):639–650, 2002.
[28] T. Shaska. Computational aspects of hyperelliptic curves. In Computer Mathematics, volume 10 of Lecture Notes Ser. Comput., pages 248–257. World Sci. Publishing, River Edge, NJ, 2003.
[29] Tanush Shaska. Determining the automorphism group of a hyperelliptic curve. In Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pages 248–254 (electronic), New York, 2003. ACM.
[30] Tony Shaska. Genus 2 curves with (3, 3)-split Jacobian and large automorphism group. In Algorithmic Number Theory (Sydney, 2002), volume 2369 of Lecture Notes in Comput. Sci., pages 205–218. Springer, Berlin, 2002.
[31] Paul B. van Wamelen. Computing with the analytic Jacobian of a genus 2 curve. In Discovering Mathematics with Magma, volume 19 of Algorithms Comput. Math., pages 117–135. Springer, Berlin, 2006.
[32] Alexander Zvonkin. Megamaps: Construction and examples. In Discrete Models: Combinatorics, Computation, and Geometry (Paris, 2001), Discrete Math. Theor. Comput. Sci. Proc., AA, pages 329–339 (electronic). Maison Inform. Math. Discrèt. (MIMD), Paris, 2001.

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