Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A hyperplane restriction theorem for holomorphic mappings and its
  application for the gap conjecture   We established a hyperplane restriction theorem for the local holomorphic
mappings between projective spaces, which is inspired by the corresponding
theorem of Green for homogeneous ideals in polynomial rings. Our theorem allows
us to give the first proof for the existence of gaps (albeit smaller) at all
level for the rational proper maps between complex unit balls, conjectured by
Huang-Ji-Yin. In addition, our proof does not distinguish the unit balls from
other generalized balls and thus it simultaneously demonstrates the same
phenomenon for all generalized balls.

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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an