Nóra Viola Harrach: Resultant method in higher dimensions

I present the Szonyi-Weiner lemma, and the Resultant method which 
proves it works with polynomials in two variables. They can be 
used to obtain results on finite projective planes. Clearly if we want 
to obtain similar results in higher dimensional projective spaces, we 
need a generalization of the methods to multivariate polynomials. I try 
to present such a generalization and applications of it.