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Question. Let $V$ be a complex projective manifold of general type (we can even assume that the canonical bundle of $V$ is ample). Suppose $\varphi: V\to V$ is a non-identical automorphism. Can $\varphi$ be isotopic to the identity map (i.e. $\varphi\in Diff_0(V)$)? I hope the answer is no, and this can be easily proven when $K(V)$ K_V$ is very ample. More generally what restrictions are known on smooth manifolds that admit self-diffeos of finite order that are isotopic to identity? |
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Finite order automorphisms of complex projective manifolds isotopic to identityQuestion. Let $V$ be a complex projective manifold of general type (we can even assume that the canonical bundle of $V$ is ample). Suppose $\varphi: V\to V$ is a non-identical automorphism. Can $\varphi$ be isotopic to the identity map (i.e. $\varphi\in Diff_0(V)$)? I hope the answer is no, and this can be easily proven when $K(V)$ is very ample. More generally what restrictions are known on smooth manifolds that admit self-diffeos of finite order that are isotopic to identity?
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