Details
| Original language | English |
|---|---|
| Number of pages | 35 |
| Journal | Journal of Algebra |
| Volume | 555 |
| Early online date | 31 Mar 2020 |
| Publication status | Published - 1 Aug 2020 |
Abstract
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of Algebra, Vol. 555, 01.08.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Hypersurfaces with defect
AU - Lindner, Niels
PY - 2020/8/1
Y1 - 2020/8/1
N2 - A projective hypersurface X⊆Pn has defect if hi(X)≠hi(Pn) for some i∈{n,…,2n−2} in a suitable cohomology theory. This occurs for example when X⊆P4 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.
AB - A projective hypersurface X⊆Pn has defect if hi(X)≠hi(Pn) for some i∈{n,…,2n−2} in a suitable cohomology theory. This occurs for example when X⊆P4 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.
UR - http://www.scopus.com/inward/record.url?scp=85082651916&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2020.02.022
DO - 10.1016/j.jalgebra.2020.02.022
M3 - Article
AN - SCOPUS:85082651916
VL - 555
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -