Geodesic
Periods of elliptic surfaces with $p_g=q=1$
Forum of Mathematics, Sigma, Tome 12 (2024)

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We prove that the period mapping is dominant for elliptic surfaces over an elliptic curve with $12$ nodal fibers, and that its degree is larger than $1$. This settles the final case of infinitesimal Torelli for a generic elliptic surface. 
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     author = {Philip Engel and Fran\c{c}ois Greer and Abigail Ward},
     title = {Periods of elliptic surfaces with $p_g=q=1$},
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Philip Engel; François Greer; Abigail Ward. Periods of elliptic surfaces with $p_g=q=1$. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.85

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