The resultant divisor is negative

Abstract

Fix two integers $1\le d<e$. We study the birational geometry of a parameter space for pairs of homogeneous polynomials of degrees $d$ and $e$ in two variables (in which the higher degree polynomial is well defined only up to a multiple of the lower degree polynomial). We show that one can run the MMP on this space, and that it eventually contracts the resultant divisor.

This article replaces and supersedes arXiv:1212.4862. 26 pages