Higher index Fano varieties with finitely many birational automorphisms. Issue 11 (2nd November 2022)
- Record Type:
- Journal Article
- Title:
- Higher index Fano varieties with finitely many birational automorphisms. Issue 11 (2nd November 2022)
- Main Title:
- Higher index Fano varieties with finitely many birational automorphisms
- Authors:
- Chen, Nathan
Stapleton, David - Abstract:
- Abstract : A famous problem in birational geometry is to determine when the birational automorphism group of a Fano variety is finite. The Noether–Fano method has been the main approach to this problem. The purpose of this paper is to give a new approach to the problem by showing that in every positive characteristic, there are Fano varieties of arbitrarily large index with finite (or even trivial) birational automorphism group. To do this, we prove that these varieties admit ample and birationally equivariant line bundles. Our result applies the differential forms that Kollár produces on $p$ -cyclic covers in characteristic $p > 0$ .
- Is Part Of:
- Compositio mathematica. Volume 158:Issue 11(2022)
- Journal:
- Compositio mathematica
- Issue:
- Volume 158:Issue 11(2022)
- Issue Display:
- Volume 158, Issue 11 (2022)
- Year:
- 2022
- Volume:
- 158
- Issue:
- 11
- Issue Sort Value:
- 2022-0158-0011-0000
- Page Start:
- 2033
- Page End:
- 2045
- Publication Date:
- 2022-11-02
- Subjects:
- Fano varieties -- hypersurfaces -- birational automorphisms -- rigidity
14E07 -- 14E05 -- 14M20
Mathematics -- Periodicals
510 - Journal URLs:
- http://journals.cambridge.org/action/displayJournal?jid=COM ↗
- DOI:
- 10.1112/S0010437X22007771 ↗
- Languages:
- English
- ISSNs:
- 0010-437X
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 3366.000000
British Library STI - ELD Digital Store - Ingest File:
- 24451.xml