Non Kählerian equivariant compactifications of an algebraic multiplicative group (Q5956599)
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scientific article; zbMATH DE number 1710129
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non Kählerian equivariant compactifications of an algebraic multiplicative group |
scientific article; zbMATH DE number 1710129 |
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Non Kählerian equivariant compactifications of an algebraic multiplicative group (English)
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21 February 2002
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group actions
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compact holomorphic manifolds
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algebraic groups
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Let \(X\) be a smooth compact complex manifold which is a compactification of \((\mathbb{C}^*)^n\). We have \(\dim(\text{Alb}(X))\leq h^{1,0} (X) \leq b_1(X)/2\leq h^{0,1}(X)\). If \(X\) is Kähler, then all the inequalities are equalities.NEWLINENEWLINENEWLINEFor every pair \((p,q)\) of integers such that \(0\leq p<q\) the authors construct a compactification \(X\) such that \(\text{Alb}(X)=\{0\}\), \(h^{1,0} (X)=p\) and \(h^{0,1}(X)=q\).
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