Let ${\mathcal{E}}^{⁎}$ be a finite complex of locally free sheaves on a complex manifold X. We prove that to every connection of type $(1,0)$ on ${\mathcal{E}}^{⁎}$ it is canonically associated an $L_{\infty }$ morphism$g:A_X^{0,⁎}(\mathcal{H}o{m}_{{\mathcal{O}}_X}^{⁎}({\mathcal{E}}^{⁎},{\mathcal{E}}^{⁎}))⇝\frac{A_X^{⁎,⁎}}{A_X^{\ge 2,⁎}}[2]$ that lifts the 1-component of the Buchweitz-Flenner semiregularity map. An application to deformations of coherent sheaves on projective manifolds is given.

中文翻译：

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半正则映射的连接和L _∞提升

让 ${\mathcal{乙}}^{⁎}$是复流形X上局部自由滑轮的有限复形。我们证明对于每一个类型的连接$(1,0)$ 上 ${\mathcal{乙}}^{⁎}$ 它规范地关联了一个 ${升}_{\infty }$ 态射$G：{\mathrm{一种}}_X^{0,⁎}(\mathcal{H}○{米}_{{\mathcal{哦}}_X}^{⁎}({\mathcal{乙}}^{⁎},{\mathcal{乙}}^{⁎}))⇝\frac{{\mathrm{一种}}_X^{⁎,⁎}}{{\mathrm{一种}}_X^{\ge 2,⁎}}[2]$这提升了 Buchweitz-Flenner 半正则映射的 1 分量。给出了投影流形上相干滑轮变形的应用。