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

Complex Manifolds (2016)

- Volume: 3, Issue: 1, page 16-40
- ISSN: 2300-7443

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topKwokwai Chan, and Yat-Hin Suen. "A differential-geometric approach to deformations of pairs (X, E)." Complex Manifolds 3.1 (2016): 16-40. <http://eudml.org/doc/276492>.

@article{KwokwaiChan2016,

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.},

author = {Kwokwai Chan, Yat-Hin Suen},

journal = {Complex Manifolds},

keywords = {deformation of holomorphic vector bundles},

language = {eng},

number = {1},

pages = {16-40},

title = {A differential-geometric approach to deformations of pairs (X, E)},

url = {http://eudml.org/doc/276492},

volume = {3},

year = {2016},

}

TY - JOUR

AU - Kwokwai Chan

AU - Yat-Hin Suen

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

JO - Complex Manifolds

PY - 2016

VL - 3

IS - 1

SP - 16

EP - 40

AB - 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.

LA - eng

KW - deformation of holomorphic vector bundles

UR - http://eudml.org/doc/276492

ER -

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