From 0f62678f523d8a0497c997161e60b3dde61ae83b Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Fri, 18 Dec 2020 16:23:58 +0100 Subject: Reassure the reader we are not done. --- bezout.tex | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) (limited to 'bezout.tex') diff --git a/bezout.tex b/bezout.tex index d7f6399..ff6fcdc 100644 --- a/bezout.tex +++ b/bezout.tex @@ -343,9 +343,10 @@ This is, to this order, precisely the Bézout bound, the maximum number of solutions that $N$ equations of degree $p-1$ may have \cite{Bezout_1779_Theorie}. That we saturate this bound is perhaps not surprising, since the coefficients of our polynomial equations -\eqref{eq:polynomial} are complex and have no symmetries. Analogous asymptotic -scaling has been found for the number of pure Higgs states in supersymmetric -quiver theories \cite{Manschot_2012_From}. +\eqref{eq:polynomial} are complex and have no symmetries. Reaching Bézout in +\eqref{eq:bezout} is not our main result, but it provides a good check. +Analogous asymptotic scaling has been found for the number of pure Higgs states +in supersymmetric quiver theories \cite{Manschot_2012_From}. More insight is gained by looking at the count as a function of $a$, defined by $\overline{\mathcal N}(\kappa,\epsilon,a)=e^{Nf(a)}$. In the large-$N$ limit, -- cgit v1.2.3-54-g00ecf