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luke naylor latex documents
research
Max Destabilizer Rank
Commits
e11d499d
Commit
e11d499d
authored
1 year ago
by
Luke Naylor
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Antony feedback: change m to q since it is rational, not integer
parent
8a9c3b9c
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main.tex
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e11d499d
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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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