We explicitly construct a genus-3 Lefschetz fibration over \({\mathbb {S}}^{2}\), whose total space is \({\mathbb {T}}^{2}\times {\mathbb {S}}^{2}\# 6\overline{{{\mathbb {C}}}{{\mathbb {P}}}^{2}}\) using the monodromy of Matsumoto’s genus-2 Lefschetz fibration. We then construct more genus-3 Lefschetz fibrations, whose total spaces are exotic minimal symplectic 4-manifolds \(3 {{\mathbb {C}}}{{\mathbb {P}}}^{2} \# q\overline{{{\mathbb {C}}}{{\mathbb {P}}}^{2}}\) for \(q=13,\ldots ,19\). We also generalize our construction to get genus-3k Lefschetz fibration structure on the 4-manifold \(\Sigma _{k}\times {\mathbb {S}}^{2}\# 6\overline{{{\mathbb {C}}}{{\mathbb {P}}}^{2}}\) using the generalized Matsumoto’s genus-2k Lefschetz fibration. From this generalized version, we derive further exotic 4-manifolds via Luttinger surgery and twisted fiber sum.

我们在\（{\ mathbb {S}} ^ {2} \）上显式构造第3类Lefschetz纤维化，其总空间为\（{\ mathbb {T}} ^ {2} \ times {\ mathbb {S }} ^ {2} \＃6 \ overline {{{\ mathbb {C}}} {{\ mathbb {P}}} ^ {2}} \}），则使用了松本2类Lefschetz纤维化的单驱。然后，我们构造更多属3的Lefschetz纤维化，其总空间为奇异的最小辛4流形\（3 {{\ mathbb {C}}} {{\ mathbb {P}}} ^ {2} \＃q \ overline {{{\ mathbb {C}}} {{\ mathbb {P}}} ^ {2}} \）代表\（q = 13，\ ldots，19 \）。我们还推广了施工得到属-3 ķ上的4个歧管莱夫谢茨纤维化结构\（\西格玛_ {K} \倍{\ mathbb {S}} ^ {2} \＃6 \划线{{{\ mathbb {C}}} {{\ mathbb {P}}} ^ {2}} \）使用广义的Matsumoto属2 k Lefschetz纤维化。从这个广义的版本中，我们通过Luttinger手术和加捻的纤维总和进一步获得了奇异的4流形。