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Commit e11d499d authored by Luke Naylor's avatar Luke Naylor
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Antony feedback: change m to q since it is rational, not integer

parent 8a9c3b9c
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......@@ -163,19 +163,19 @@ $\chern(F)$, and so we can write:
beta_min = var("beta", domain="real")
c_lower_bound = -(ts(beta=beta_min).rank(u)/ts().alpha).expand() + c
var("m", domain="real")
c_val = c_lower_bound + m
var("q", domain="real")
c_val = c_lower_bound + q
\end{sagesilent}
\begin{equation}
\label{eqn-cintermsofm}
c=\chern_1(E) = \sage{c_val}
\qquad 0 \leq m \leq \chern_1^{\beta_{-}}(F)
\qquad 0 \leq q \leq \chern_1^{\beta_{-}}(F)
\end{equation}
Furthermore, $\chern_1 \in \ZZ$ so we only need to consider
$m \in \frac{1}{n} \ZZ \cap [0, \chern_1^{\beta_{-}}(F)]$.
For the next subsections, we consider $m$ to be fixed with one of these values,
$q \in \frac{1}{n} \ZZ \cap [0, \chern_1^{\beta_{-}}(F)]$.
For the next subsections, we consider $q$ to be fixed with one of these values,
and we shall be varying $\chern_0(E) = r$ to see when certain inequalities fail.
......
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