A differential-geometric approach to deformations of pairs (X, E)

Abstract: This article gives an exposition of the deformation theory for pairs (X, E), where X is a compact complex manifold and E is a holomorphic vector bundle over X, adapting an analytic viewpoint `a la Kodaira- Spencer. By introducing and exploiting an auxiliary differential operator, we derive the Maurer–Cartan equation and differential graded Lie algebra (DGLA) governing the deformation problem, and express them in terms of differential-geometric notions such as the connection and curvature of E, obtaining a chain level refinement of the classical results that the tangent space and obstruction space of the moduli problem are respectively given by the first and second cohomology groups of the Atiyah extension of E over X. As an application, we give examples where deformations of pairs are unobstructed.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: A differential-geometric approach to deformations of pairs (X, E) ; volume:3 ; number:1 ; year:2016 ; extent:25 ; Complex manifolds ; 3, Heft 1 (2016) (gesamt 25)

Contributors, Places and Time

• Creator: Chan, Kwokwai ; Suen, Yat-Hin

Further information

• DOI: 10.1515/coma-2016-0002
• URN: urn:nbn:de:101:1-2410281503356.402035154285
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:30 AM CEST