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corrected definition of CY threefold
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Khedir
Khedir
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Let $X$ be a rigid Calabi-Yau varietythreefold. Does $X$ have only finitely many automorphisms?

N.B. A smooth projective varietythreefold $X$ over $\mathbb C$ is a rigid Calabi-Yau variety if $h^i(X,\mathcal O_X) =0$ for all $i>0$, $K_X$ is numerically trivial and $\mathrm{H}^1(X,T_X) =0$ (or equivalently $h^{2,1}(X) = 0$).

Let $X$ be a rigid Calabi-Yau variety. Does $X$ have only finitely many automorphisms?

N.B. A smooth projective variety $X$ over $\mathbb C$ is a rigid Calabi-Yau variety if $h^i(X,\mathcal O_X) =0$ for all $i>0$ and $\mathrm{H}^1(X,T_X) =0$ (or equivalently $h^{2,1}(X) = 0$).

Let $X$ be a rigid Calabi-Yau threefold. Does $X$ have only finitely many automorphisms?

N.B. A smooth projective threefold $X$ over $\mathbb C$ is a rigid Calabi-Yau variety if $h^i(X,\mathcal O_X) =0$ for all $i>0$, $K_X$ is numerically trivial and $\mathrm{H}^1(X,T_X) =0$ (or equivalently $h^{2,1}(X) = 0$).

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Khedir
Khedir
  • 23
  • 3

Can a rigid CY threefold have infinitely many automorphisms

Let $X$ be a rigid Calabi-Yau variety. Does $X$ have only finitely many automorphisms?

N.B. A smooth projective variety $X$ over $\mathbb C$ is a rigid Calabi-Yau variety if $h^i(X,\mathcal O_X) =0$ for all $i>0$ and $\mathrm{H}^1(X,T_X) =0$ (or equivalently $h^{2,1}(X) = 0$).