STRICT INCLUSIONS OF HIGH RANK LOCI
Résumé
For a given projective variety X, the high rank loci are the closures of
the sets of points whose X-rank is higher than the generic one. We show examples of
strict inclusion arising from two consecutive high rank loci. Our rst example comes
from looking at the Veronese surface of plane quartics. Although Piene had already
shown an example in which X is a curve, we construct innitely many curves in P4
for which such strict inclusion appears. For space curves, we give two criteria to check
whether the locus of points of maximum rank 3 is nite (possibly empty).
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