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Let $X$ be a smooth weak fano threesfold arising as the blowup of a smooth curve $C$ of degree and genus $(d,g)=(10,2)$ in a rank 1 smooth fano Threefoldthreefold $Y$, $-K_Y^3 = 22$. Let $H$ be a hyperplane in $X$ and $E$ the exceptional divisor. What is $h^0(X, 4H-5E)$?

I think it can be 1 or 3, but not sure how to compute it directly.

Let $X$ be a smooth weak fano threesfold arising as the blowup of a smooth curve $C$ of degree and genus $(d,g)=(10,2)$ in a smooth fano Threefold $Y$, $-K_Y^3 = 22$. Let $H$ be a hyperplane in $X$ and $E$ the exceptional divisor. What is $h^0(X, 4H-5E)$?

I think it can be 1 or 3, but not sure how to compute it directly.

Let $X$ be a smooth weak fano threesfold arising as the blowup of a smooth curve $C$ of degree and genus $(d,g)=(10,2)$ in a rank 1 smooth fano threefold $Y$, $-K_Y^3 = 22$. Let $H$ be a hyperplane in $X$ and $E$ the exceptional divisor. What is $h^0(X, 4H-5E)$?

I think it can be 1 or 3, but not sure how to compute it directly.

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$h^0(X, 4H-5E)$ on Weakweak Fano Threefoldthreefold

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user15720
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$h^0(X, 4H-5E)$ on Weak Fano Threefold

Let $X$ be a smooth weak fano threesfold arising as the blowup of a smooth curve $C$ of degree and genus $(d,g)=(10,2)$ in a smooth fano Threefold $Y$, $-K_Y^3 = 22$. Let $H$ be a hyperplane in $X$ and $E$ the exceptional divisor. What is $h^0(X, 4H-5E)$?

I think it can be 1 or 3, but not sure how to compute it directly.