Projective and affine structures in positive characteristic I: Chern class formulas and Characterizations of projective spaces
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911692761333760 |
|---|---|
| author | Wakabayashi, Yasuhiro |
| author_facet | Wakabayashi, Yasuhiro |
| contents | This paper aims to develop a theory of projective and affine structures on higher-dimensional varieties in positive characteristic. This theory deals with Frobenius-projective and Frobenius-affine structures, which have been previously investigated in the case where the underlying space is a curve. We first provide a description of such structures in terms of Berthelot's higher-level differential operators. That description leads us to obtain a positive characteristic version of Gunning's formulas, which give necessary conditions on Chern classes for the existence of Frobenius-projective and Frobenius-affine structures, respectively. Finally, we establish some characterizations of projective spaces using Frobenius-projective structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_04846 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Projective and affine structures in positive characteristic I: Chern class formulas and Characterizations of projective spaces Wakabayashi, Yasuhiro Algebraic Geometry Number Theory This paper aims to develop a theory of projective and affine structures on higher-dimensional varieties in positive characteristic. This theory deals with Frobenius-projective and Frobenius-affine structures, which have been previously investigated in the case where the underlying space is a curve. We first provide a description of such structures in terms of Berthelot's higher-level differential operators. That description leads us to obtain a positive characteristic version of Gunning's formulas, which give necessary conditions on Chern classes for the existence of Frobenius-projective and Frobenius-affine structures, respectively. Finally, we establish some characterizations of projective spaces using Frobenius-projective structures. |
| title | Projective and affine structures in positive characteristic I: Chern class formulas and Characterizations of projective spaces |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2011.04846 |