Cubic hypersurfaces with positive dual defects
Algebraic Geometry
2018-10-19 v4
Abstract
We show that if a cubic hypersurface with positive dual defect over the complex number field is not a cone, then either the hypersurface coincides with the secant variety of the singular locus, or the hypersurface contains a linear subvariety of dimension greater than the dual defect such that the intersection of the singular locus and a general contact locus is contained in the linear subvariety.
Keywords
Cite
@article{arxiv.1806.03429,
title = {Cubic hypersurfaces with positive dual defects},
author = {Katsuhisa Furukawa},
journal= {arXiv preprint arXiv:1806.03429},
year = {2018}
}
Comments
20 pages; v3: revised the statement of the main result and proofs