scholarly journals Integral Kähler invariants and the Bergman kernel asymptotics for line bundles

2017 ◽  
Vol 308 ◽  
pp. 348-403
Author(s):  
Spyros Alexakis ◽  
Kengo Hirachi
Keyword(s):  
Bergman Kernel ◽  
Line Bundles ◽  
Bergman Kernel Asymptotics

scholarly journals A direct approach to Bergman kernel asymptotics for positive line bundles

2008 ◽  
Vol 46 (2) ◽  
pp. 197-217 ◽  
Author(s):  
Robert Berman ◽  
Bo Berndtsson ◽  
Johannes Sjöstrand
Keyword(s):  
Bergman Kernel ◽  
Direct Approach ◽  
Line Bundles ◽  
Bergman Kernel Asymptotics ◽  
Positive Line

scholarly journals Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves

2017 ◽  
Vol 4 (1) ◽  
pp. 7-15 ◽  
Author(s):  
Robert Xin Dong
Keyword(s):  
Elliptic Curves ◽  
Bergman Kernel ◽  
Complex Structure ◽  
Elliptic Functions ◽  
Hyperelliptic Curves ◽  
Asymptotic Formulas ◽  
Holomorphic Family ◽  
Structure Information ◽  
Taylor Expansions ◽  
Bergman Kernel Asymptotics

Abstract We survey variations of the Bergman kernel and their asymptotic behaviors at degeneration. For a Legendre family of elliptic curves, the curvature form of the relative Bergman kernel metric is equal to the Poincaré metric on ℂ \ {0,1}. The cases of other elliptic curves are either the same or trivial. Two proofs depending on elliptic functions’ special properties and Abelian differentials’ Taylor expansions are discussed, respectively. For a holomorphic family of hyperelliptic nodal or cuspidal curves and their Jacobians, we announce our results on the Bergman kernel asymptotics near various singularities. For genus-two curves particularly, asymptotic formulas with precise coefficients involving the complex structure information are written down explicitly.

Bergman kernel asymptotics for generalized Fock spaces

2001 ◽  
Vol 83 (1) ◽  
pp. 207-242 ◽  
Author(s):  
Finbarr Holland ◽  
Richard Rochberg
Keyword(s):  
Bergman Kernel ◽  
Fock Spaces ◽  
Bergman Kernel Asymptotics

scholarly journals THE FIRST COEFFICIENTS OF THE ASYMPTOTIC EXPANSION OF THE BERGMAN KERNEL OF THESpincDIRAC OPERATOR

2006 ◽  
Vol 17 (06) ◽  
pp. 737-759 ◽  
Author(s):  
XIAONAN MA ◽  
GEORGE MARINESCU
Keyword(s):  
Asymptotic Expansion ◽  
Bergman Kernel ◽  
Dirac Operators ◽  
Line Bundles ◽  
Tensor Powers

We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spincDirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending [15]. We compute the second coefficient b1in the asymptotic expansion using the method of [24].

Sign in / Sign up

Export Citation Format

Share Document