Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicity of the saturated special fiber ring of height two perfect
  ideals   Let $R$ be a polynomial ring and $I \subset R$ be a perfect ideal of height
two minimally generated by forms of the same degree. We provide a formula for
the multiplicity of the saturated special fiber ring of $I$. Interestingly,
this formula is equal to an elementary symmetric polynomial in terms of the
degrees of the syzygies of $I$. Applying ideas introduced in arXiv:1805.05180,
we obtain the value of the j-multiplicity of $I$ and an effective method for
determining the degree and birationality of rational maps defined by
homogeneous generators of $I$.

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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn