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• W1616615900 abstract "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 $jgeq 0$, $i>0$ 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]." @default.
• W1616615900 created "2016-06-24" @default.
• W1616615900 creator A5077121399 @default.
• W1616615900 date "2006-10-30" @default.
• W1616615900 modified "2023-09-27" @default.
• W1616615900 title "Hodge Cohomology Criteria For Affine Varieties" @default.
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• W1616615900 hasPublicationYear "2006" @default.
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