On Todorov surfaces
Carlos Rito
Departamento de Matemática
Universidade de Trás-os Montes e Alto Douro

Resumo

Let S be a Todorov surface, i.e., a minimal smooth surface of general type with q=0 and p_g=1 having an involution i such that S/i is birational to a K3 surface and such that the bicanonical map of S is composed with i. In this talk I will show that, if P is the minimal smooth model of S/i, then P is the minimal desingularization of a double cover of the projective plane branched over two cubics. Furthermore, given a Todorov surface S, it is possible to construct Todorov surfaces S_j with self-intersection of the canonical divisor between 1 and K_S2-1 and such that P is also the smooth minimal model of S_j/i_j, where i_j is the involution of S_j.

Encontro Matemático SPM/CIM em Geometria Algébrica