Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Recovering plane curves from their bitangents

Authors: Lucia Caporaso and Edoardo Sernesi
Journal: J. Algebraic Geom. 12 (2003), 225-244
Published electronically: October 17, 2002
MathSciNet review: 1949642
Full-text PDF

Abstract | References | Additional Information

Abstract: We prove that a general complex projective plane quartic curve is uniquely determined by its 28 bitangent lines. A similar property (called theta-property in the paper) is proved for a general singular quartic having $\delta=1,\dots,4$ double points with respect to its set of generalized bitangents (suitably defined). The proofs are by degeneration.

References [Enhancements On Off] (What's this?)

  • [AF1] Aluffi, P. - Faber, C.: Plane curves with small linear orbits II. International J. of Math. 11 (2000), 591-608.
  • [AF2] Aluffi, P. - Faber, C.: Linear orbits of arbitrary plane curves. Mich. Math. J. (W.Fulton issue) 48 (2000), 1-37.
  • [ACGH] Arbarello - Cornalba - Griffiths - Harris: Geometry of Algebraic Curves, I. Grund. series, vol. 267, Springer.
  • [E-Ch] Enriques, F. - Chisini, O.: Teoria geometrica delle equazioni e delle funzioni algebriche, vol. I. Zanichelli, Bologna 1929.
  • [H] Harris, J.: Theta-characteristics on algebraic curves. Trans. AMS 271 (1982), pp. 611-638.
  • [K-W] Krazer, A. - Wirtinger, W.: Abelsche Funktionen und Allgemeine Thetafunktionen. Enc. d. Math. Wiss. II B 7, Leipzig 1921.
  • [GIT] Mumford, D. - Fogarty, J. - Kirwan, F.: Geometric Invariant Theory. (Third edition) E.M.G. 34 Springer 1994.
  • [S] Segre, C.: Le molteplicità nelle intersezioni delle curve piane algebriche con alcune applicazioni ai principii della teoria di tali curve. Giornale di Matematiche 36 (1898), 1-50. Opere, vol. I, 380-429.
  • [W] Walker, R.J.: Algebraic Curves. Princeton U.P. 1950.
  • [Z] Zariski, O.: Dimension-theoretic characterization of maximal irreducible algebraic systems of plane nodal curves of a given order $n$ and with a given number $d$ of nodes. Am. J. Math. 104 (1982), pp. 209-226.

Additional Information

Lucia Caporaso
Affiliation: Università degli Studi del Sannio, Benevento, Italy; Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Address at time of publication: Dipartimento di Matematica, Università Roma Tre, L.Go S.L. Murialdo 1, 00146 Roma, Italy

Edoardo Sernesi
Affiliation: Dipartimento di Matematica, Università Roma Tre, L.Go S.L. Murialdo 1, 00146 Roma, Italy

Received by editor(s): September 15, 2000
Published electronically: October 17, 2002