  The four- and five-dimensional effective actions of Calabi-Yau threefold
compactifications are derived with a focus on terms involving up to four
space-time derivatives. The starting points for these reductions are the ten-
and eleven-dimensional supergravity actions supplemented with the known
eight-derivative corrections that have been inferred from Type II string
amplitudes. The corrected background solutions are determined and the
fluctuations of the Kahler structure of the compact space and the form-field
background are discussed. It is concluded that the two-derivative effective
actions for these fluctuations only takes the expected supergravity form if
certain additional ten- and eleven-dimensional higher-derivative terms for the
form-fields are included. The main results on the four-derivative terms include
a detailed treatment of higher-derivative gravity coupled to Kahler structure
deformations. This is supplemented by a derivation of the vector sector in
reductions to five dimensions. While the general result is only given as an
expansion in the fluctuations, a complete treatment of the one-Kahler modulus
case is presented for both Type II theories and M-theory.
