Article contents
ON THE SHARPNESS OF TIAN’S CRITERION FOR K-STABILITY
Published online by Cambridge University Press: 23 October 2020
Abstract
Tian’s criterion for K-stability states that a Fano variety of dimension n whose alpha invariant is greater than
${n}{/(n+1)}$
is K-stable. We show that this criterion is sharp by constructing n-dimensional singular Fano varieties with alpha invariants
${n}{/(n+1)}$
that are not K-polystable for sufficiently large n. We also construct K-unstable Fano varieties with alpha invariants
${(n-1)}{/n}$
.
MSC classification
- Type
- Article
- Information
- Copyright
- © Foundation Nagoya Mathematical Journal, 2020
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220428005253308-0230:S0027763020000288:S0027763020000288_inline1627.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220428005253308-0230:S0027763020000288:S0027763020000288_inline1628.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220428005253308-0230:S0027763020000288:S0027763020000288_inline1629.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220428005253308-0230:S0027763020000288:S0027763020000288_inline1630.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220428005253308-0230:S0027763020000288:S0027763020000288_inline1632.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220428005253308-0230:S0027763020000288:S0027763020000288_inline1633.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220428005253308-0230:S0027763020000288:S0027763020000288_inline1634.png?pub-status=live)
- 3
- Cited by