What's the best (or your favourite) definition of a morphism of a quasi projective variety? I've seen a huge number of equivalent definitions, and I'd like to know which is the best to memorise! 


I'd prefer to have a definition that doesn't mention sheaves/schemes or rational maps (since I normally define a rational map as a morphism on an open set, and don't want my definitions to be circular).


Many thanks in advance!



Algebraic Geometry - Definition of a Morphism
A regular map $\phi: X \to Y$ of quasi-projective varieties is a continuous map with respect to the Zariski topology such that for $V \subset Y$ an open set and $f$ a regular function on $V$, we have $f\circ \phi$ is regular on $\phi^{-1}V$. This seems to me to be to be exactly what you would want and quite intuitive and understandable. 


