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luke naylor latex documents
research
Max Destabilizer Rank
Commits
fde6e979
Commit
fde6e979
authored
1 year ago
by
Luke Naylor
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Add justificatiosn for problem 2
parent
90dd4611
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1 year ago
Stage: test
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main.tex
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-5
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fde6e979
...
...
@@ -560,8 +560,7 @@ are trying to solve for.
\begin{problem}
[sufficiently large `left' pseudo-walls]
\label
{
problem:problem-statement-1
}
Fix a Chern character
$
v
$
with positive rank,
$
\Delta
(
v
)
\geq
0
$
,
and
$
\beta
_{
-
}
(
v
)
\in
\QQ
$
.
Fix a Chern character
$
v
$
with positive rank, and
$
\Delta
(
v
)
\geq
0
$
.
The goal is to find all pseudo-semistabilizers
$
u
$
which give circular pseudo-walls containing some fixed point
$
P
\in\Theta
_
v
^
-
$
.
...
...
@@ -598,13 +597,18 @@ $v-u$ for each solution $u$ of the problem.
Fix a Chern character
$
v
$
with positive rank,
$
\Delta
(
v
)
\geq
0
$
,
and
$
\beta
_{
-
}
(
v
)
\in
\QQ
$
.
The goal is to find all solutions
$
u
=(
r,c
\ell
,d
\ell
^
2
)
$
The goal is to find all solutions
$
u
$
to problem
\ref
{
problem:problem-statement-1
}
with the choice
$
P
=(
\beta
_{
-
}
,
0
)
$
.
This will give all circular pseudo-walls left of
$
V
_
v
$
.
\end{problem}
This is a specialization of problem (
\ref
{
problem:problem-statement-1
}
)
which will give all circular pseudo-walls left of
$
V
_
v
$
.
This is because all circular walls left of
$
V
_
v
$
intersect
$
\Theta
_
v
^
-
$
.
The
$
\beta
_{
-
}
(
v
)
\in
\QQ
$
condition is to ensure that there are finitely many
solutions. As mentioned in the introduction (
\ref
{
sec:intro
}
), this is known,
however this will also be proved again in passing in this article.
\section
{
B.Schmidt's Solutions to the Problems
}
...
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