  Consider the holomorphic bundle with connection on $\mathbb
P^1-\{0,1,\infty\}$ corresponding to the regular hypergeometric differential
operator \[
  \prod_{j=1}^h(D-\alpha_j)-z\prod_{j=1}^h(D-\beta_j), \qquad D=z\frac{d}{dz}.
\] If the numbers $\alpha_i$ and $\beta_j$ are real and for all $i$ and $j$ the
number $\alpha_i-\beta_j$ is not integer, then the bundle with connection is
known to underlie a complex polarizable variation of Hodge structures. We
calculate some Hodge invariants for this variation, in particular, the Hodge
numbers. From this we derive a conjecture of Corti and Golyshev. We also use
non-abelian Hodge theory to interpret our theorem as a statement about
parabolic Higgs bundles.
