  We study non-degenerate and degenerate (extremal) Killing horizons of
arbitrary geometry and topology within the Einstein-Maxwell-dilaton model with
a Liouville potential (the EMdL model) in d-dimensional (d>=4) static
space-times. Using Israel's description of a static space-time, we construct
the EMdL equations and the space-time curvature invariants: the Ricci scalar,
the square of the Ricci tensor, and the Kretschmann scalar. Assuming that
space-time metric functions and the model fields are real analytic functions in
the vicinity of a space-time horizon, we study behavior of the space-time
metric and the fields near the horizon and derive relations between the
space-time curvature invariants calculated on the horizon and geometric
invariants of the horizon surface. The derived relations generalize the similar
relations known for horizons of static four and 5-dimensional vacuum and
4-dimensional electrovacuum space-times. Our analysis shows that all the
extremal horizon surfaces are Einstein spaces. We present necessary conditions
for existence of static extremal horizons within the EMdL model.
