Complex sentence: Serre showed that "h" 0 (Ω) may differ from "h" 1 ("O"), and Igusa that they may be equal but still exceed the irregularity defined as the dimension of the Picard variety.
Split into simpler sentences: Serre showed that "h" 0 (Ω) may differ from "h" 1 ("O"). Igusa showed that even when they are equal, they may be greater than the irregularity defined as the dimension of the Picard variety.