From db5f3be28619ab11e63386136ca0fd2006d8b4a3 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Wed, 15 Mar 2023 18:02:45 +0000
Subject: [PATCH] Make progress on first proper slide
---
Makefile | 1 +
main.tex | 84 +++++++++++++++++++---------------------
sagetexscripts/fig1.sage | 14 +++----
3 files changed, 47 insertions(+), 52 deletions(-)
diff --git a/Makefile b/Makefile
index def6666..2f7e0e4 100644
--- a/Makefile
+++ b/Makefile
@@ -26,6 +26,7 @@ $(addsuffix .py,${SAGEPLOTFILES}): $(addsuffix .sage,${SAGEPLOTFILES})
.PHONY: clean
clean:
+ rm -rf **/__pycache__
latexmk -C
git clean -xf || echo no git repo to use for cleaning
diff --git a/main.tex b/main.tex
index d363e3f..4d56b94 100644
--- a/main.tex
+++ b/main.tex
@@ -26,6 +26,8 @@
\newcommand\coh{\operatorname{Coh}}
\newcommand\rank{\operatorname{rk}}
\newcommand\degree{\operatorname{deg}}
+\newcommand\realpart{\mathfrak{Re}}
+\newcommand\imagpart{\mathfrak{Im}}
\begin{document}
@@ -36,22 +38,6 @@
\section{Transitioning to Stab on Triangulated Categories}
\begin{frame}{Central Charge}
- \begin{column}{.5\textwidth}
- \centering
- one
- \\
- one
- \\
- one
- \\
- one
- \\
- \end{column}
-
- \begin{column}{.4\textwidth}
- \centering
- two
- \end{column}
\end{frame}
\begin{sagesilent}
@@ -60,44 +46,52 @@
\begin{frame}{Central Charge for Mumford Stability}
\begin{align*}
- \centralcharge \colon \coh(X) &\to \CC \\
- E &\mapsto - \degree(E) + i \rank(E)
+ &\centralcharge \colon \coh(X) \to \CC \\
+ &\centralcharge (E) = - \degree(E) + i \rank(E)
\end{align*}
-
- \begin{column}{.5\textwidth}
- \centering
- one
- \end{column}
-
- \begin{column}{.4\textwidth}
- \centering
- two
- \end{column}
-
\resizebox{1\hsize}{!}{
\sageplot{sagetexscripts.fig1.plot()}
}
- \begin{column}{.5\textwidth}
- \centering
- one
- \\
- one
- \\
- one
- \\
- one
- \\
- \end{column}
-
- \begin{column}{.4\textwidth}
- \centering
- two
- \end{column}
+ \begin{columns}[T] % align columns
+ \begin{column}{.48\linewidth}
+ \[
+ \centralcharge (E) = r(E) e^{i\pi \varphi(E)}
+ \]
+ $\varphi$ called "phase"
+ \end{column}%
+ %\hfill%
+ \begin{column}{.48\linewidth}
+ \[
+ \mu(E) =
+ \frac{
+ - \realpart(\centralcharge(E))
+ }{
+ \imagpart(\centralcharge(E))
+ }
+ \quad
+ \text{(allow for $+\infty$)}
+ \]
+ \end{column}%
+ \end{columns}
\end{frame}
+
+\begin{frame}
+ \begin{columns}[T] % align columns
+ \begin{column}{.48\linewidth}
+ Left Part
+ \end{column}%
+ \hfill%
+ \begin{column}{.48\linewidth}
+
+ Right Part
+ \end{column}%
+ \end{columns}
+\end{frame}
+
\section{Section 1}
\section{Section 2}
diff --git a/sagetexscripts/fig1.sage b/sagetexscripts/fig1.sage
index 30a5826..d749238 100644
--- a/sagetexscripts/fig1.sage
+++ b/sagetexscripts/fig1.sage
@@ -25,14 +25,14 @@ def plot():
return point(
Z,
marker = "o",
- size = 600,
+ size = 800,
rgbcolor = "white",
#markeredgecolor = "purple",
zorder = 100
) + point(
Z,
marker = name,
- size = 500,
+ size = 700,
rgbcolor = "red",
zorder = 101
) + line(
@@ -53,11 +53,11 @@ def plot():
p = sum(
plot_central_charge(chern, name)
for chern, name in [
- (O1, r"$\mathcal{O}(1)$"),
- (O, r"$\mathcal{O}_X$"),
- (O1inv, r"$\mathcal{O}(-1)$"),
- (O2, r"$\mathcal{O}(2)$"),
- (O_x, r"$\mathcal{O}_p$")
+ (O1, r"$\mathcal{Z}(\mathcal{O}(1))$"),
+ (O, r"$\mathcal{Z}(\mathcal{O}_X)$"),
+ (O1inv, r"$\mathcal{Z}(\mathcal{O}(-1))$"),
+ (O2, r"$\mathcal{Z}(\mathcal{O}(2))$"),
+ (O_x, r"$\mathcal{Z}(\mathcal{O}_p)$")
]
)
--
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