diff --git a/main.tex b/main.tex index 259a22b91685c40e1879a857c7a894037f1b8d8f..c3f8668e93786dbc80b95169597bee39cc8fc930 100644 --- a/main.tex +++ b/main.tex @@ -554,6 +554,12 @@ Suppose we take $\beta = \beta_{-}$ (so that $\chern^{\beta}_2(F)=0$) in the previous subsections, to find all circular walls to the left of the vertical wall (TODO as discussed in ref). +% redefine \beta (especially coming from rendered SageMath expressions) +% to be \beta_{-} for the rest of this subsubsection +\bgroup +\let\originalbeta\beta +\renewcommand\beta{{\originalbeta_{-}}} + \begin{align} d &\geq& \sage{bgmlv1_d_lowerbound_linear_term} @@ -573,7 +579,7 @@ vertical wall (TODO as discussed in ref). Furthermore, we get an extra bound for $d$ resulting from the condition that the radius of the circular wall must be positive. As discussed in (TODO ref), this -is equivalent to $\chern^{\beta_{-}}_2(E) > 0$, which yields: +is equivalent to $\chern^{\beta}_2(E) > 0$, which yields: \begin{sagesilent} positive_radius_condition = ( @@ -589,7 +595,7 @@ is equivalent to $\chern^{\beta_{-}}_2(E) > 0$, which yields: \begin{equation*} \sage{positive_radius_condition} \end{equation*} - +\egroup \section{Conclusion}