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Mar 5, 2023 at 19:19 comment added Daniele A The isomorphism $\tau^*E \cong E$ induces an involution $\tau^*\colon H^0(E)\to H^0(E)$. The zero locus $D$ is $\tau$-invariant if the corresponding section of $H^0(E)$ is either invariant or anti-invariant. So a general $D$ will not be invariant but you can find one that is.
Mar 5, 2023 at 12:58 history asked user41650 CC BY-SA 4.0