$L_{\infty}$ liftings of semiregularity maps via Chern-Simons classes
Ruggero Bandiera, Emma Lepri, Marco Manetti
TL;DR
This paper introduces Chern-Simons classes for curved DG-pairs and demonstrates their application in providing canonical $L_ infty$ liftings of semiregularity maps for coherent sheaves on complex manifolds, advancing deformation theory.
Contribution
It develops a new framework of Chern-Simons classes for curved DG-pairs and applies it to lift semiregularity maps in a canonical way.
Findings
Chern-Simons classes are defined for curved DG-pairs.
Canonical $L_ infty$ liftings of semiregularity maps are constructed.
The approach links Chern-Simons classes with deformation theory of coherent sheaves.
Abstract
We introduce the notion of Chern-Simons classes for curved DG-pairs and we prove that a particular case of this general construction provides canonical liftings of Buchweitz-Flenner semiregularity maps for coherent sheaves on complex manifolds.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology