Deformations of rational curves in positive characteristic
-
Kazuhiro Ito
,
Tetsushi Ito
Abstract
We study deformations of rational curves and their singularities
in positive characteristic.
We use this to prove that if a smooth and proper surface
in positive characteristic p is dominated by a family of rational curves
such that one member has all δ-invariants (resp. Jacobian numbers)
strictly less than
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 18J22191
Award Identifier / Grant number: 20674001
Award Identifier / Grant number: 26800013
Funding statement:
Funding statement: The first named author is supported by Research Fellowships of Japan Society for the Promotion of Science for Young Scientists KAKENHI Grant Number 18J22191. The second named author is supported by the JSPS KAKENHI Grant Number 20674001 and 26800013. The third named author is supported by the ERC Consolidator Grant 681838 K3CRYSTAL.
Acknowledgements
The authors thank Frank Gounelas and Ichiro Shimada for comments and discussion. The authors thank Hiromu Tanaka for providing invaluable information on the geometry of surfaces over imperfect fields and references. Moreover, the authors thank Gert-Martin Greuel for many comments and suggestions, including a whole report on an earlier version of this article. Finally, the authors thank the referee for remarks and comments, which improve the article.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Restriction formula and subadditivity property related to multiplier ideal sheaves
- Proper Lie groupoids are real analytic
- Deformations of rational curves in positive characteristic
- Curved Rickard complexes and link homologies
- Boundary properties of fractional objects: Flexibility of linear equations and rigidity of minimal graphs
Articles in the same Issue
- Frontmatter
- Restriction formula and subadditivity property related to multiplier ideal sheaves
- Proper Lie groupoids are real analytic
- Deformations of rational curves in positive characteristic
- Curved Rickard complexes and link homologies
- Boundary properties of fractional objects: Flexibility of linear equations and rigidity of minimal graphs
