Monodromy representations and surfaces with maximal Albanese dimension

Abstract

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

16 pages, 1 figure. v3: Final version. Bollettino dell'Unione Matematica Italiana (2017)

References in corpus (2)

• A family of surfaces with $p_g=q=2,K^2=7$ and Albanese map of degree $3$
• A pair of rigid surfaces with $p_g=q=2$ and $K^2=8$ whose universal cover is not the bidisk

Cited by in corpus (1)

• Representations of braid groups and construction of projective surfaces