On cubics and quartics through a canonical curve
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 2 (2003) no. 4, p. 803-822

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

Classification:  14H60,  14H42
@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},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 2},
number = {4},
year = {2003},
pages = {803-822},
zbl = {1110.14029},
mrnumber = {2040644},
language = {en},
url = {http://www.numdam.org/item/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, Serie 5, Volume 2 (2003) no. 4, pp. 803-822. http://www.numdam.org/item/ASNSP_2003_5_2_4_803_0/

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