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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
@article{ASNSP_2003_5_2_4_803_0,
author = {Pauly, Christian},
title = {On cubics and quartics through a canonical curve},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {803--822},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 2},
number = {4},
year = {2003},
mrnumber = {2040644},
zbl = {1110.14029},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_803_0/}
}
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 SP - 803 EP - 822 VL - 2 IS - 4 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_803_0/ LA - en ID - ASNSP_2003_5_2_4_803_0 ER -
%0 Journal Article %A Pauly, Christian %T On cubics and quartics through a canonical curve %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2003 %P 803-822 %V 2 %N 4 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_803_0/ %G en %F ASNSP_2003_5_2_4_803_0
Pauly, Christian. On cubics and quartics through a canonical curve. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 4, pp. 803-822. http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_803_0/