$Connections and $L_{\infty}$ liftings of semiregularity maps$

Connections and $L_{\infty}$ liftings of semiregularity maps

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 $g\colon A^{0, *}_X(\mathcal{H}om^*_{O_X}(E^*,E^*))\to \dfrac{A^{*,*}_X}{A^{\ge 2,*}_X}[2]$ th...

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Veröffentlicht in:	arXiv.org 2021-05
Hauptverfasser:	Lepri, Emma, Manetti, Marco
Format:	Artikel
Sprache:	eng
Schlagworte:	Colon Manifolds Sheaves
Online-Zugang:	Volltext
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Zusammenfassung:	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.
ISSN:	2331-8422

Zusammenfassung:	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.
ISSN:	2331-8422

Connections and \(L_{\infty}\) liftings of semiregularity maps