Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hodge Cohomology Criteria For Affine Varieties   We give several new criteria for a quasi-projective variety to be affine. In
particular, we prove that an algebraic manifold $Y$ with dimension $n$ is
affine if and only if $H^i(Y, \Omega^j_Y)=0$ for all $j\geq 0$, $i>0$ and
$\kappa(D, X)=n$, i.e., there are $n$ algebraically independent nonconstant
regular functions on $Y$, where $X$ is the smooth completion of $Y$, $D$ is the
effective boundary divisor with support $X-Y$ and $\Omega^j_Y$ is the sheaf of
regular $j$-forms on $Y$. This proves Mohan Kumar's affineness conjecture for
algebraic manifolds and gives a partial answer to J.-P. Serre's Steinness
question \cite{36} in algebraic case since the associated analytic space of an
affine variety is Stein [15, Chapter VI, Proposition 3.1].

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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an