# On osculating cones and the Riemann-Kempf singularity theorem for hyperelliptic curves, trigonal curves, and smooth plane quintics

Fabio Bardelli; Luisella Verdi

Compositio Mathematica (1988)

- Volume: 65, Issue: 2, page 177-199
- ISSN: 0010-437X

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topBardelli, Fabio, and Verdi, Luisella. "On osculating cones and the Riemann-Kempf singularity theorem for hyperelliptic curves, trigonal curves, and smooth plane quintics." Compositio Mathematica 65.2 (1988): 177-199. <http://eudml.org/doc/89888>.

@article{Bardelli1988,

author = {Bardelli, Fabio, Verdi, Luisella},

journal = {Compositio Mathematica},

keywords = {Jacobian; hyperelliptic curve; trigonal curve; plane quintic; osculating cone; Torelli theorem},

language = {eng},

number = {2},

pages = {177-199},

publisher = {Kluwer Academic Publishers},

title = {On osculating cones and the Riemann-Kempf singularity theorem for hyperelliptic curves, trigonal curves, and smooth plane quintics},

url = {http://eudml.org/doc/89888},

volume = {65},

year = {1988},

}

TY - JOUR

AU - Bardelli, Fabio

AU - Verdi, Luisella

TI - On osculating cones and the Riemann-Kempf singularity theorem for hyperelliptic curves, trigonal curves, and smooth plane quintics

JO - Compositio Mathematica

PY - 1988

PB - Kluwer Academic Publishers

VL - 65

IS - 2

SP - 177

EP - 199

LA - eng

KW - Jacobian; hyperelliptic curve; trigonal curve; plane quintic; osculating cone; Torelli theorem

UR - http://eudml.org/doc/89888

ER -

## References

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- [B.V.] F. Bardelli and L. Verdi, Un'osservazione sul teorema di singolarità di Riemann-Kempf per curve iperellittiche e trigonali, Boll. Un. Mat. It. (6) 5-A (1986) 201-204. Zbl0595.14018MR850288
- [G.H.] P.A. Griffiths and J. Harris, Principles of Algebraic Geometry, WileyInterscience Publ. (Pure and applied Math.), J. Wiley & Sons (1978). Zbl0408.14001MR507725
- [K] G. Kempf, On the geometry of a theorem of Riemann, Ann. of Math.98 (1973) 178-185. Zbl0275.14023MR349687
- [K.2] G. Kempf, The equations defining a curve of genus four, A.M.S. Proceedings 97,2 June 1986, Providence R.I. Zbl0595.14021MR835869
- [S.D.] B. Saint-Donat, On Petri's analysis of the linear system of quadrics through a canonical curve, Math. Ann.206 (1973) 157-175. Zbl0315.14010MR337983
- [Se.R.] J.G. Semple and L. Roth, Introduction to Algebraic Geometry, OxfordClarendon Press (1949). Zbl0041.27903MR34048
- [Sh.] I.R. Shafarevic, Basic Algebraic Geometry, Grundlehren der Math. Wiss.213, Springer Verlag, Berlin, Heidelberg, New York (1977). Zbl0284.14001MR447223

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