385 research outputs found
On cubics and quartics through a canonical curve
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.Comment: 16 page
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