Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves

• Autorzy: Robert Xin Dong
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

variation of Bergman kernel; degeneration of hyperelliptic curve; node; cusp

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2017
• Tom: 4
• Numer: 1
• Strony: 7-15

Daty

wydano

2017-02-01

online

2017-02-08

Twórcy

autor

Robert Xin Dong

• Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, 464-8602 Nagoya,

Identyfikatory

DOI

10.1515/coma-2017-0002