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K-stable divisors in $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^2$ of degree $(1,1,2)$

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arxiv 2206.08539 v2 pith:NZDOFPC6 submitted 2022-06-17 math.AG

classification math.AG
keywords mathbbtimesdegreek-stabledivisordivisorseveryprove
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abstract

We prove that every smooth divisor in $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^2$ of degree $(1,1,2)$ is K-stable.

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  1. On K-stability of $\mathbb P^3$ blown up along a smooth genus $2$ curve of degree $5$

    math.AG 2024-12 conditional novelty 6.0 of 10

    K-stability is established for infinitely many smooth members of Fano threefold family 2.19, with the main theorem giving a lower bound on local stability thresholds away from one open subset of the exceptional divisor.

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