In this article, we construct a family of genus Lefschetz fibrations with , , and by applying a single lantern substitution to the twisted fiber sums of Matsumoto’s genus Lefschetz fibration over . Moreover, we compute the fundamental group of and show that it is isomorphic to the trivial group if or , if , and for all integers . Also, we prove that our fibrations admit section, that their total spaces are symplectically minimal, and that they have symplectic Kodaira dimension . In addition, using techniques developed over the past decade with other authors, we also construct the genus Lefschetz fibrations over with and via the fiber sums of Matsumoto’s and Xiao’s genus Lefschetz fibrations, and present some applications in constructing exotic smooth structures on small -manifolds with and .
"Genus Lefschetz fibrations with and ." Kyoto J. Math. 60 (4) 1419 - 1451, December 2020. https://doi.org/10.1215/21562261-2019-0067