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.
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| Author: | Niels LindnerORCiD |
|---|---|
| Document Type: | Article |
| Parent Title (English): | Journal of Algebra |
| Volume: | 555 |
| First Page: | 1 |
| Last Page: | 35 |
| Year of first publication: | 2020 |
| ArXiv Id: | http://arxiv.org/abs/1610.04077 |
| DOI: | https://doi.org/10.1016/j.jalgebra.2020.02.022 |
