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

• Autorzy: Kwokwai Chan , Yat-Hin Suen
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2016
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-09-02

zaakceptowano

2016-01-21

online

2016-02-01

Twórcy

autor

Kwokwai Chan

• Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

autor

Yat-Hin Suen

• Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

Identyfikatory

DOI

10.1515/coma-2016-0002