diff --git a/main.tex b/main.tex index c560ce7c6545100a27f8cf5299667fb3385cf17e..63d5c71cc0a9c50851f34eb68ab32a540115ab63 100644 --- a/main.tex +++ b/main.tex @@ -154,6 +154,8 @@ $\chern(E) = (r,c,d)$ of some semistabilizer $E$. v = Chern_Char(*var("R C D", domain="real")) u = Chern_Char(*var("r c d", domain="real")) + + Δ = lambda v: v.Q_tilt() \end{sagesilent} Recall [ref] that $\chern_1^{\beta_{-}}$ has fixed bounds in terms of @@ -185,7 +187,8 @@ and we shall be varying $\chern_0(E) = r$ to see when certain inequalities fail. This condition expressed in terms of $R,C,D,r,c,d$ looks as follows: \begin{sagesilent} - bgmlv1 = - u.Q_tilt() - (v-u).Q_tilt() + v.Q_tilt() + # First Bogomolov-Gieseker form expression that must be non-negative: + bgmlv1 = Δ(v) - Δ(u) - Δ(v-u) \end{sagesilent} \begin{equation}