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- Title
On the Hessian of Cubic Hypersurfaces.
- Authors
Bricalli, Davide; Favale, Filippo Francesco; Pirola, Gian Pietro
- Abstract
In this paper, we analyze the Hessian locus associated to a general cubic hypersurface, by describing its singular locus and its desingularization for every dimension. The strategy is based on strong connections between the Hessian and the quadrics defined as partial derivatives of the cubic polynomial. In particular, we focus our attention on the singularities of the Hessian hypersurface associated to the general cubic four-fold. It turns out to be a minimal surface of general type: its analysis is developed by exploiting the nature of this surface as a degeneracy locus of a symmetric vector bundle map and by describing an unramified double cover, which is constructed in a more general setting.
- Subjects
HYPERSURFACES; LOCUS (Mathematics); VECTOR bundles; MINIMAL surfaces; VECTOR data; QUADRICS
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 10, p8672
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad324