The non rationality of the generic Enriques' threefold
Luciana Picco Botta, Alessandro Verra (1983)
Compositio Mathematica
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Displaying similar documents to “Canonical curves and quadrics of rank 4”
The non rationality of the generic Enriques' threefold
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Elliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7.
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On cubics and quartics through a canonical curve
Christian Pauly (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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