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Li Yutong
Li Yutong
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Is an anticanonical Weil divisor in $\mathbb{Q}$-GoresteinGorenstein variety Calabi-Yau?

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Li Yutong
Li Yutong
  • 3.5k
  • 16
  • 34

Let $P$ be a normal, $\mathbb{Q}$-Gorestein variety with terminal singularities. Let $X \subseteq P$ be a normal, irreducible Weil divisor such that $X \sim_{\mathbb{Q}} - K_P$, that is $\mathbb{Q}$-linearly equivalent to the anticanonical divisor of $P$ (which is $\mathbb{Q}$-Cartier) .

My question is, does $X$ have trivial$\mathbb{Q}$-trivial canonical divisor? In the adjuction formula for Weil divosr, it seems there is a $Diff$ term appears. I was wondering if this term is zero here?

Let $P$ be a normal, $\mathbb{Q}$-Gorestein variety with terminal singularities. Let $X \subseteq P$ be a normal, irreducible Weil divisor such that $X \sim_{\mathbb{Q}} - K_P$, that is $\mathbb{Q}$-linearly equivalent to the anticanonical divisor of $P$ (which is $\mathbb{Q}$-Cartier) .

My question is, does $X$ have trivial canonical divisor? In the adjuction formula for Weil divosr, it seems there is a $Diff$ term appears. I was wondering if this term is zero here?

Let $P$ be a normal, $\mathbb{Q}$-Gorestein variety with terminal singularities. Let $X \subseteq P$ be a normal, irreducible Weil divisor such that $X \sim_{\mathbb{Q}} - K_P$, that is $\mathbb{Q}$-linearly equivalent to the anticanonical divisor of $P$ (which is $\mathbb{Q}$-Cartier) .

My question is, does $X$ have $\mathbb{Q}$-trivial canonical divisor? In the adjuction formula for Weil divosr, it seems there is a $Diff$ term appears. I was wondering if this term is zero here?

Source Link
Li Yutong
Li Yutong
  • 3.5k
  • 16
  • 34

Is an anticanonical Weil divisor in $\mathbb{Q}$-Gorestein variety Calabi-Yau?

Let $P$ be a normal, $\mathbb{Q}$-Gorestein variety with terminal singularities. Let $X \subseteq P$ be a normal, irreducible Weil divisor such that $X \sim_{\mathbb{Q}} - K_P$, that is $\mathbb{Q}$-linearly equivalent to the anticanonical divisor of $P$ (which is $\mathbb{Q}$-Cartier) .

My question is, does $X$ have trivial canonical divisor? In the adjuction formula for Weil divosr, it seems there is a $Diff$ term appears. I was wondering if this term is zero here?