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arXiv · 2601.11474

The resultant divisor is negative

Olivier Benoist
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Abstract

Fix two integers $1\leq d<e$. 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.

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Olivier Benoist. 2026-01-16. The resultant divisor is negative. https://arxiv.org/abs/2601.11474

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