The Hodge number h^1,1 of irregular algebraic surfaces
  We prove a new inequality for the Hodge number h^1,1 of irregular complex smooth projective surfaces of general type without irregular pencils of genus >1. More specifically we show that if the irregularity q satisfies q=2^k+1 then h^1,1>4q-4. 
Andrea Causin, Margarida Mendes Lopes and Gian Pietro Pirola
math.AG