The enumerative geometry of cubic hypersurfaces: point and line conditions
Publisher DOI
Abstract
The set of smooth cubic hypersurfaces in Pn is an open subset of a projective space. A compactification of the latter which allows to count the number of smooth cubic hypersurfaces tangent to a prescribed number of lines and passing through a given number of points is termed a 1–complete variety of cubic hypersurfaces, in analogy with the space of complete quadrics. Imitating the work of Aluffi for plane cubic curves, we construct such a space in arbitrary dimensions by a sequence of five blow-ups. The counting problem is then reduced to the computation of five total Chern classes. In the end, we derive the desired numbers in the case of cubic surfaces.
Date Issued
2024
Publication Type
Article
Subject(s)
Language(s)
en
Author(s)
Belotti, Mara | |
Fevola, Claudia | |
Kretschmer, Andreas |
Additional Credits
Journal
Collectanea Mathematica
Publisher
Springer
ISSN
0010-0757
2038-4815
Access(Rights)
open.access