Monodromy representations and surfaces with maximal Albanese dimension

摘要: We relate the existence of some surfaces general type and maximal Albanese dimension to monodromy representations braid group $\mathsf{B}_2(C_2)$ in symmetric $\mathsf{S}_n$. Furthermore, we compute number such up $n=9$, analyze cases $n \in \{2, \, 3, 4\}$. For $n=2, 3$ recover with $p_g=q=2$ recently studied (with different methods) by author his collaborators, whereas for $n=4$ obtain conjecturally new examples.