On <a href="https://mathoverflow.net/questions/20077/how-would-you-encourage-graduate-students-to-learn-algebraic-geometry-and-or-comp">another thread</a> I asked how I could encourage my final year undergraduate colleagues to take an algebraic geometry or complex analysis courses during their graduate studies.

Willie Wong proposed me following idea - to show them some interesting results in this fields with relatively simply proofs and some consequences in other fields.
Thus by 'interesting' result in algebraic geometry I here mean the result which may convince 3rd year undergraduate student to study algebraic geometry.

In fact I'm supposed to give some talk during the seminar dedicated to final year undergraduates, and I can propose my own topic, so I thought that it could work.
But my problem is that I'm just wanna-be student of algebraic geometry and I don't have enough insight and knowledge to find a topic which 'could work'.

Also I doubt whether it is possible to present some intriguing ideas of algebraic geometry to audience without any preparation in this field.

So in short my first question is as above:
>Is it possible to present some intriguing ideas of algebraic geometry to audience without any preparation in this field?

To be more precise - the talk should take a one or two meetings, 90 minutes each one.
The audience will be, as I said 3rd year undergraduate students, all of them after two semester course in algebra, some of them after one or two semesters in commutative algebra. All taking the course in one complex variable, and after one semester introductory course in differential geometry.
Some of them may be interested in number theory.

The second, related question is as follows:

>If You think that the answer to the previuos question is positive, please try to give an example of idea/theorem/result which would be accessible in such time for such audience, and which You find interesting enough to make them consider possibility of studying algebraic geometry. Try to think about the results which shows connections of AG with some other fields of mathematics.