On cubics and quartics through a canonical curve

Christian Pauly

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2003)

  • Volume: 2, Issue: 4, page 803-822
  • ISSN: 0391-173X

Abstract

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We construct families of quartic and cubic hypersurfaces through a canonical curve, which are parametrized by an open subset in a grassmannian and a Flag variety respectively. Using G. Kempf’s cohomological obstruction theory, we show that these families cut out the canonical curve and that the quartics are birational (via a blowing-up of a linear subspace) to quadric bundles over the projective plane, whose Steinerian curve equals the canonical curve

How to cite

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Pauly, Christian. "On cubics and quartics through a canonical curve." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 2.4 (2003): 803-822. <http://eudml.org/doc/84520>.

@article{Pauly2003,
abstract = {We construct families of quartic and cubic hypersurfaces through a canonical curve, which are parametrized by an open subset in a grassmannian and a Flag variety respectively. Using G. Kempf’s cohomological obstruction theory, we show that these families cut out the canonical curve and that the quartics are birational (via a blowing-up of a linear subspace) to quadric bundles over the projective plane, whose Steinerian curve equals the canonical curve},
author = {Pauly, Christian},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {803-822},
publisher = {Scuola normale superiore},
title = {On cubics and quartics through a canonical curve},
url = {http://eudml.org/doc/84520},
volume = {2},
year = {2003},
}

TY - JOUR
AU - Pauly, Christian
TI - On cubics and quartics through a canonical curve
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2003
PB - Scuola normale superiore
VL - 2
IS - 4
SP - 803
EP - 822
AB - We construct families of quartic and cubic hypersurfaces through a canonical curve, which are parametrized by an open subset in a grassmannian and a Flag variety respectively. Using G. Kempf’s cohomological obstruction theory, we show that these families cut out the canonical curve and that the quartics are birational (via a blowing-up of a linear subspace) to quadric bundles over the projective plane, whose Steinerian curve equals the canonical curve
LA - eng
UR - http://eudml.org/doc/84520
ER -

References

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  6. [Gr] M. Green, Quadrics of rank four in the ideal of the canonical curve, Invent. Math. 75 (1984), 85-104. Zbl0542.14018MR728141
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  8. [K1] G. Kempf, “Abelian Integrals”, Monografias Inst. Mat. No. 13, Univ. Nacional Autónoma Mexico, 1984. Zbl0541.14023MR743421
  9. [K2] G. Kempf, The equation defining a curve of genus 4 , Proc. of the Amer. Math. Soc. 97 (1986), 214-225. Zbl0595.14021MR835869
  10. [KS] G. Kempf – F.-O. Schreyer, A Torelli theorem for osculating cones to the theta divisor, Compositio Math. 67 (1988), 343-353. Zbl0665.14018MR959216
  11. [OPP] W. M. Oxbury – C. Pauly – E. Previato, Subvarieties of 𝒮𝒰 C ( 2 ) and 2 θ -divisors in the Jacobian, Trans. Amer. Math. Soc., Vol. 350 (1998), 3587-3614. Zbl0898.14014MR1467474
  12. [PP] C. Pauly – E. Previato, Singularities of 2 θ -divisors in the Jacobian, Bull. Soc. Math. France 129 (2001), 449-485. Zbl1016.14013MR1881203
  13. [We] G. Welters, The surface C - C on Jacobi varieties and second order theta functions, Acta Math. 157 (1986), 1-22. Zbl0771.14012MR857677

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