Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moduli Spaces for Dynamical Systems with Portraits   A $\textit{portrait}$ $\mathcal{P}$ on $\mathbb{P}^N$ is a pair of finite
point sets $Y\subseteq{X}\subset\mathbb{P}^N$, a map $Y\to X$, and an
assignment of weights to the points in $Y$. We construct a parameter space
$\operatorname{End}_d^N[\mathcal{P}]$ whose points correspond to degree $d$
endomorphisms $f:\mathbb{P}^N\to\mathbb{P}^N$ such that $f:Y\to{X}$ is as
specified by a portrait $\mathcal{P}$, and prove the existence of the GIT
quotient moduli space
$\mathcal{M}_d^N[\mathcal{P}]:=\operatorname{End}_d^N//\operatorname{SL}_{N+1}$
under the $\operatorname{SL}_{N+1}$-action
$(f,Y,X)^\phi=\bigl(\phi^{-1}\circ{f}\circ\phi,\phi^{-1}(Y),\phi^{-1}(X)\bigr)$
relative to an appropriately chosen line bundle. We also investigate the
geometry of $\mathcal{M}_d^N[\mathcal{P}]$ and give two arithmetic
applications.

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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: stat