Completely Decomposable Jacobian Varieties in New Genera

References

• [Akbas and Singerman 90] M. Akbas and D. Singerman. “The Normalizer of Γ0(N) in PSL(2, R).” Glasg. Math. J. 32: 3 (1990), 317–327.
   Google Scholar
• [Behn et al. 13] A. Behn, R. E. Rodríguez, and A. M. Rojas. “Adapted Hyperbolic Polygons and Symplectic Representations for Group Actions on Riemann Surfaces.” J. Pure Appl. Algebra 217 (2013), 409–426. http://www.geometry.uchile.cl.
   Web of Science ®Google Scholar
• [Behn et al. 15] A. Behn, C. Muñoz, and A. M. Rojas. “Classification of Topologically Non-equivalent Actions using Generating Vectors, A SAGE Package.” Preprint available from (http://www.geometry.uchile.cl), (2015).
   Google Scholar
• [Birkenhake and Lange 04] Ch. Birkenhake and H. Lange. Complex Abelian Varieties. Second edition. Grundlehren Math. Wiss. 302. Berlin, Heidelberg: Springer, 2004.
   Google Scholar
• [Bosma et al. 97] W. Bosma, J. Cannon, and C. Playoust. “The Magma Algebra System. I. The User Language.” J. Symbolic Comput. 24 (1997), 235–265. http://magma.maths.usyd.edu.au
   Web of Science ®Google Scholar
• [Breuer 00] T. Breuer. Characters and Automorphism Groups of Compact Riemann Surfaces. London Math. Soc. Lecture Note Ser., Vol. 280. Cambridge: Cambridge University Press, 2000.
   Google Scholar
• [Broughton 90] S. A. Broughton. “Classifying Finite Group Actions on Surfaces of Low Genus.” J. Pure Appl. Algebra 69 (1990), 233–270.
   Web of Science ®Google Scholar
• [Carocca and Rodríguez 06] A. Carocca and R. E. Rodríguez. “Jacobians with Group Actions and Rational Idempotents.” J. Algebra 306 (2006), 322–343.
   Web of Science ®Google Scholar
• [Carocca et al. 14] A. Carocca, R. E. Rodríguez and A. M. Rojas. “Symmetric Group Actions on Jacobian Varieties.” Contemp. Math. 629 (2014), 43–57.
   Google Scholar
• [Conder 10] M. Conder. “Group Actions on Surfaces.” Available online (https://www.math.auckland.ac.nz/conder/), 2010.
   Google Scholar
• [Conder 14] M. D. E. Conder. “Large Group Actions on Surfaces.” In Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces, pp. 77–97, Contemp. Math. 629. Providence, RI: Amer. Math. Soc., 2014.
   Google Scholar
• [Curtis and Reiner 62] C. W. Curtis and I. Reiner. Representation Theory of Finite Groups and Associative Algebras. Pure and Applied Mathematics, Vol. XI. New York-London: Interscience Publishers, a division of John Wiley & Sons, 1962.
   Google Scholar
• [Earle 06] C. Earle. “The Genus Two Jacobians That Are Isomorphic to a Product of Elliptic Curves.” Contemp. Math. 397 (2006), 27–36.
   Google Scholar
• [Ekedahl and Serre 93] T. Ekedahl and J.-P. Serre. “Exemples de courbes algébriques à jacobienne complètement décomposable.” C. R. Math. Acad. Sci. Paris Sér. I. 317: 5 (1993), 509–513.
   Google Scholar
• [Farkas and Kra 92] H. M. Farkas and I. Kra. “Riemann Surfaces.” Grad. Texts Math. 71, Second edition. New York: Springer-Verlag, 1992.
   Google Scholar
• [Frediani et al. 15] P. Frediani, A. Ghigi, and M. Penegini. “Shimura Varieties in the Torelli Locus via Galois Coverings.” Int. Math. Res. Not. 20 (2015), 10595–10623.
   Web of Science ®Google Scholar
• [Harvey 71] W. J. Harvey. “On Branch Loci in Teichmüller Space.” Trans. Am. Math. Soc. 153 (1971), 387–399.
   Web of Science ®Google Scholar
• [Kani 94] E. Kani. “Elliptic Curves on Abelian Surfaces.” Manuscripta Math. 84 (1994), 199–223.
   Web of Science ®Google Scholar
• [Kenku and Momose 88] M. A. Kenku and F. Momose. “Automorphism Groups of the Modular Curves X0(N).” Compos. Math. 65: 1 (1988), 51–80.
   Web of Science ®Google Scholar
• [Lange and Recillas 04] H. Lange and S. Recillas. “Abelian Varieties with Group Actions.” J. Reine Angew. Math. 575 (2004), 135–155.
   Web of Science ®Google Scholar
• [Lange and Rojas 12] H. Lange and A. M. Rojas. “Polarizations of Isotypical Components of Jacobians with Group Action.” Arch. Math. 98 (2012), 513–526.
   Web of Science ®Google Scholar
• [Magaard et al. 09] K. Magaard, T. Shaska, and H. Völklein. “Genus 2 Curves That Admit A Degree 5 Map to an Elliptic Curve.” Forum Math. 3 (2009), 547–566.
   Google Scholar
• [Moonen and Oort 11] B. Moonen and F. Oort. “The Torelli Locus and Special Subvarieties.” Handbook Moduli 2 (2011), 549–594.
   Google Scholar
• [Muñoz 14] C. Muñoz. “Clasificación topológica de acciones de grupos en Superficies de Riemann. Un método algebraico.” Master Thesis, Universidad de Chile, 2014. https://sites.google.com/a/u.uchile.cl/polygons/
   Google Scholar
• [Nakajima 07] R. Nakajima. “On Splitting of Certain Jacobian Varieties.” J. Math. Kyoto Univ. 47: 2 (2007), 391–415.
   Google Scholar
• [Paulhus 15] J. Paulhus. “Branching Data for Curves up to Genus 48.” arXiv:1512.07657 [math.AG] at http://arxiv.org/abs/1512.07657, 2015.
   Google Scholar
• [Paulhus 08] J. Paulhus. “Decomposing Jacobians of Curves with Extra Automorphisms.” Acta Arith. 132 (2008), 231–244.
   Web of Science ®Google Scholar
• [Paulhus and Rojas 15] J. Paulhus and A. M. Rojas. “Completely Decomposable Jacobian Variety Data.” Available online (http://www.math.grinnell.edu/paulhusj/completedec.html or http://www.geometry.uchile.cl), 2015.
   Google Scholar
• [Paulhus and Rojas 16] J. Paulhus and A. M. Rojas. “Magma Code to Determine Jacobian Variety Decompositions.” Available online (https://github.com/jenpaulhus/decompose-jacobians), 2016.
   Google Scholar
• [Ries 93] J. F. X. Ries. “Subvarieties of Moduli Space Determined by Finite Groups Acting on Surfaces.” Trans. Amer. Math. Soc. 335 (1993), 385–406.
   Web of Science ®Google Scholar
• [Rodríguez 14] R. E. Rodríguez. “Abelian Varieties and Group Actions.” Contemp. Math. 629 (2014), 299–314.
   Google Scholar
• [Stein et al. 15] W. A. Stein, et al. “Sage Mathematics Software (Version 6.7).” The Sage Development Team. Available online (http://www.sagemath.org), 2015.
   Google Scholar
• [Völklein 96] H. Völklein. Groups as Galois groups, Cambridge Stud. Adv. Math.53. Cambridge, UK: Cambridge University Press, 1996.
   Google Scholar
• [Yamauchi 07] T. Yamauchi. “On simple Factors of Jacobian Varieties of Modular Curves.” Yokohama Math. J. 53: 2 (2007), 149–160.
   Google Scholar