Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves

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 trivia...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autor principal:	Dong Robert Xin
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	variation of bergman kernel degeneration of hyperelliptic curve node cusp Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/263f25ef52814b709c5f1f520d3fce89
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:263f25ef52814b709c5f1f520d3fce89
record_format	dspace
spelling	oai:doaj.org-article:263f25ef52814b709c5f1f520d3fce892021-12-02T19:07:56ZBoundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves2300-744310.1515/coma-2017-0002https://doaj.org/article/263f25ef52814b709c5f1f520d3fce892017-02-01T00:00:00Zhttps://doi.org/10.1515/coma-2017-0002https://doaj.org/toc/2300-7443We 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.Dong Robert XinDe Gruyterarticlevariation of bergman kerneldegeneration of hyperelliptic curvenodecuspMathematicsQA1-939ENComplex Manifolds, Vol 4, Iss 1, Pp 7-15 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	variation of bergman kernel degeneration of hyperelliptic curve node cusp Mathematics QA1-939
spellingShingle	variation of bergman kernel degeneration of hyperelliptic curve node cusp Mathematics QA1-939 Dong Robert Xin Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
description	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.
format	article
author	Dong Robert Xin
author_facet	Dong Robert Xin
author_sort	Dong Robert Xin
title	Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
title_short	Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
title_full	Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
title_fullStr	Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
title_full_unstemmed	Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
title_sort	boundary asymptotics of the relative bergman kernel metric for hyperelliptic curves
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/263f25ef52814b709c5f1f520d3fce89
work_keys_str_mv	AT dongrobertxin boundaryasymptoticsoftherelativebergmankernelmetricforhyperellipticcurves
_version_	1718377136592519168

Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves

Ejemplares similares