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Degree of irrationality of properly elliptic surfaces
In this paper, we study the degree of irrationality of properly elliptic surfaces with a section. We prove $\min\{χ(\mathcal O_S),\,2\operatorname{gon}(C)\} \leq \operatorname{irr}(S) \leq 2\operatorname{gon}(C)$. The lower bound is obtained from the canonical bundle formula and the Cayley--Bacharac
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