Moduli spaces of quadratic pairs over compact Riemann surfaces
André Gama
Departamento de Matemática
Universidade de Trás-os Montes e Alto Douro

Resumo

We consider holomorphic quadratic pairs of type (2,d) over a compact Riemann surface X. The stability condition for these objects depends on a real parameter a, and we determine conditions on a and d for the non-emptiness of the corresponding moduli spaces N_a(2,d). Through the analysis of the changes in the spaces N_a(2,d) when the parameter a varies, and through a more detailed study of a specific space N_a_0(2,d), we study the connectedness of N_a(2,d). We shall also mention the relation between these spaces and the moduli space of reductive representations of the fundamental group of X in Sp(4,R).

Encontro Matemático SPM/CIM em Geometria Algébrica