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Hypersurfaces with defect

  • A projective hypersurface X⊆P^n has defect if h^i(X) ≠ h^i(P^n) for some i∈{n,…,2n−2} in a suitable cohomology theory. This occurs for example when X⊆P^4 is not Q-factorial. We show that hypersurfaces with defect tend to be very singular: In characteristic 0, we present a lower bound on the Tjurina number, where X is allowed to have arbitrary isolated singularities. For X with mild singularities, we prove a similar result in positive characteristic. As an application, we obtain an estimate on the asymptotic density of hypersurfaces without defect over a finite field.
Author:Niels LindnerORCiD
Document Type:Article
Parent Title (English):Journal of Algebra
First Page:1
Last Page:35
Year of first publication:2020
ArXiv Id:http://arxiv.org/abs/1610.04077
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