Hodge Cohomology Criteria For Affine Varieties
| dc.creator | Zhang, Jing | |
| dc.date | 2006-10-30 | |
| dc.date.accessioned | 2026-07-07T07:29:34Z | |
| dc.date.available | 2026-07-07T07:29:34Z | |
| dc.description | 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 $H^i(Y, Ω^j_Y)=0$ for all $j\geq 0$, $i>0$ and $κ(D, X)=n$, 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 $Ω^j_Y$ 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]. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610884 | |
| dc.identifier | http://arxiv.org/abs/math/0610884 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118161 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14J10, 14J30, 32E10 | |
| dc.title | Hodge Cohomology Criteria For Affine Varieties | |
| dc.type | text |