Genus two Lefschetz fibration with $b^{+}_{2}=1$ and ${c_1}^{2}=1$

Anar Akhmedov, Naoyuki Monden

Published 2015-09-06Version 1

In this article we construct a genus two Lefschetz fibration $f: X \rightarrow \mathbb{S}^{2}$ with $b^{+}_{2}(X)=1$ and $c_1^{2}(X)=1$ by applying a lantern substitution to the twisted fiber sum of Matsumoto's well known genus two Lefschetz fibration over $\mathbb{S}^2$. Moreover, we prove that our fibration admits $-2$ sphere section. We also show that the total space $X$ is symplectically minimal and compute it's fundamental group.