With North American plumbing standards, your "horizontal" pipe must slope towards the drain at a rate of 0.25" vertical per 12" of horizontal. Any more, or any less, is unacceptable (for different reasons). The total vertical drop during the horizontal run must be less than the inside diameter of the pipe used, so that there is always an air escape route above the flowing liquid, to keep it from sucking the drain trap dry via vacuum.

A vertical drop from the sink to the trap is fine for short distances. Dunno what "short" is defined as, but 10-20cm should be no issue.

Cheers