论文标题
$ \ bar \ partial $ - $（p，q）$ - 非还原分析空间上的表格
The $\bar\partial$-equation for $(p,q)$-forms on a non-reduced analytic space
论文作者
论文摘要
在任何纯$ n $维的，可能是非还原的，分析空间$ x $上，我们介绍了sheaves $ \ mathscr {e} _x^{p，p，q} $ spooty $ $（p，q）$ - 表单和某些扩展名$ \ m m istscr {a} _x^_x^iis sexpection in conspection sexpection n is conspection， $ \ bar \ partial $ - equient在$ \ mathscr {a} _x $中可在本地解决。或带$ \ Mathscr {a} _x^{p，q} $是平滑表单上的模块，尤其是它们是很好的滑轮。我们还在$ x $上引入了某些带束带$ \ mathscr {b} _x^{n-p，n-q} $，这些$ x $在serre duality的情况下是双dual至$ \ mathscr {a} _x^{a} _x^{p，q} $。更准确地说，我们表明，$ \ Mathscr {B}^{n-p，n-q}（x）$的紧凑型dolbeault共同体以自然的方式是$ \ mathscr {a}}^a}^{p，q}（x）（x）$的dolbeault共同学的双重偶。
On any pure $n$-dimensional, possibly non-reduced, analytic space $X$ we introduce the sheaves $\mathscr{E}_X^{p,q}$ of smooth $(p,q)$-forms and certain extensions $\mathscr{A}_X^{p,q}$ of them such that the corresponding Dolbeault complex is exact, i.e., the $\bar\partial$-equation is locally solvable in $\mathscr{A}_X$. The sheaves $\mathscr{A}_X^{p,q}$ are modules over the smooth forms, in particular, they are fine sheaves. We also introduce certain sheaves $\mathscr{B}_X^{n-p,n-q}$ of currents on $X$ that are dual to $\mathscr{A}_X^{p,q}$ in the sense of Serre duality. More precisely, we show that the compactly supported Dolbeault cohomology of $\mathscr{B}^{n-p,n-q}(X)$ in a natural way is the dual of the Dolbeault cohomology of $\mathscr{A}^{p,q}(X)$.
