The Michigan Mathematical Journal

The rank of the second Gaussian map for general curves

Alberto Calabri, Ciro Ciliberto, and Rick Miranda

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Michigan Math. J., Volume 60, Issue 3 (2011), 545-559.

First available in Project Euclid: 8 November 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)
Secondary: 14D06: Fibrations, degenerations 14H45: Special curves and curves of low genus


Calabri, Alberto; Ciliberto, Ciro; Miranda, Rick. The rank of the second Gaussian map for general curves. Michigan Math. J. 60 (2011), no. 3, 545--559. doi:10.1307/mmj/1320763048.

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  • A. Arbarello, M. Cornalba, Ph. Griffiths, and J. Harris, Geometry of algebraic curves, vol. I, Grundlehren Math. Wiss., 267, Springer-Verlag, New York, 1985.
  • A. Beauville and J.-Y. Mérindol, Sections hyperplanes des surfaces K3, Duke Math. J. 55 (1987), 873–878.
  • A. Calabri and C. Ciliberto, On special projections of varieties: Epitome to a theorem of Beniamino Segre, Adv. Geom. 1 (2001), 97–106.
  • L. Chiantini and C. Ciliberto, A few remarks on the lifting problem, Journées de géométrie algébrique d'Orsay (Orsay, 1992), Astérisque 218 (1993), 95–109.
  • C. Ciliberto, J. Harris, and R. Miranda, On the surjectivity of the Wahl map, Duke Math. J. 57 (1988), 829–858.
  • C. Ciliberto and R. Miranda, On the Gaussian map for canonical curves of low genus, Duke Math. J. 61 (1990), 417–443.
  • –––, Gaussian maps for certain families of canonical curves, Complex projective geometry (Trieste and Bergen, 1989), London Math. Soc. Lecture Note Ser., 179, pp. 106–127, Cambridge Univ. Press, Cambridge, 1992.
  • E. Colombo and P. Frediani, Some results on the second Gaussian map for curves, Michigan Math. J. 58 (2009), 745–758.
  • –––, Siegel metric and curvature of the moduli space of curves, Trans. Amer. Math. Soc. 362 (2010), 1231–1246.
  • –––, On the second Gaussian map for curves on a K3 surface, Nagoya Math. J. 199 (2010), 123–136.
  • E. Colombo, P. Frediani, and G. Pareschi, Hyperplane sections of abelian surfaces, J. Algebraic Geom. (to appear), arXiv:0903.2781.
  • E. Colombo, G. P. Pirola, and A. Tortora, Hodge–Gaussian maps, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 30 (2001), 125–146.
  • M. L. Green, Infinitesimal methods in Hodge theory, Algebraic cycles and Hodge theory (Torino, 1993), Lecture Notes in Math., 1594, pp. 1–92, Springer-Verlag, Berlin, 1994.
  • F. O. Schreyer, A standard basis approach to syzygies of canonical curves, J. Reine Angew. Math. 421 (1991), 83–123.
  • J. Wahl, The Jacobian algebra of a graded Gorenstein singularity, Duke Math. J. 55 (1987), 843–871.