Constructs examples of strict inclusions between consecutive high rank loci for Veronese varieties and infinitely many curves in P^4, with criteria for finiteness of maximal rank-3 loci on space curves.
Hartshorne, Algebraic Geometry, Springer-Verlag, Berlin–Heidelberg–New York
2 Pith papers cite this work. Polarity classification is still indexing.
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2019 2verdicts
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The authors define and investigate the minimal degree and maximal number of linearly independent minimal-degree hypersurfaces for sets of curves and surfaces not contained in lower-degree hypersurfaces, showing some results and posing open questions as variations on Halphen's theme.
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Strict inclusions of high rank loci
Constructs examples of strict inclusions between consecutive high rank loci for Veronese varieties and infinitely many curves in P^4, with criteria for finiteness of maximal rank-3 loci on space curves.
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Minimal degree equations for curves and surfaces (variations on a theme of Halphen)
The authors define and investigate the minimal degree and maximal number of linearly independent minimal-degree hypersurfaces for sets of curves and surfaces not contained in lower-degree hypersurfaces, showing some results and posing open questions as variations on Halphen's theme.