半正则映射的联络与$L_{\infty}$提升
Connections and $L_{\infty}$ liftings of semiregularity maps
摘要：
设$E^*$是复流形$X$上局部自由层的有限复形.证明了$E^*$上的每一个$(1,0)$型联络都与提升Buchweitz-Flenner半正则映射的1-分支的$L_{\infty}$态射$g\colon A^{0, *}_X(\mathcal{H}om^*_{O_X}(E^*,E^*))\to \dfrac{A^{*,*}_X}{A^{\ge 2,*}_X}[2]$正则相关.给出了射影流形上凝聚层变形的一个应用。
英文摘要：
Let $E^*$ be a finite complex of locally free sheaves on a complex manifold $X$. We prove that to every connection of type $(1,0)$ on $E^*$ it is canonically associated an $L_{\infty}$ morphism $g\colon A^{0, *}_X(\mathcal{H}om^*_{O_X}(E^*,E^*))\to \dfrac{A^{*,*}_X}{A^{\ge 2,*}_X}[2]$ that lifts the 1-component of Buchweitz-Flenner semiregularity map. An application to deformations of coherent sheaves on projective manifolds is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
