Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sarkisov links from toric weighted blowups of $\mathbb{P}^3$ and
  $\mathbb{P}^4$ at a point   We study Sarkisov links initiated by the toric weighted blowup of a point in
$\mathbb{P}^3$ or $\mathbb{P}^4$ using variation of GIT. We completely classify
which of these initiate Sarkisov links and describe the links explicitly.
Moreover, if $X$ is the toric weighted blowup of $\mathbb{P}^d$ at a point, we
give a simple criterion in terms of the weights of the blowup that
characterises when $X$ is weak Fano.

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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int