Geometric considerations of this paper are related to $N=2$ Superconformal Field Theories (SCFT). There is a version of the above data and axioms for SCFT. In particular, each $H^{p,q}$ is a hermitian super vector space. There is an action of the super extension of the product of Virasoro and anti-Virasoro algebra on $H$. In the discussion of the moduli spaces below we will not distinguish between CFTs and SCFTs, because except of some minor details, main conclusions are true in both cases.