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Degenerating Riemann Surfaces and the Quillen Metric

Dennis Eriksson (Institutionen för matematiska vetenskaper, matematik)
International mathematics research notices (1073-7928). 2, p. 347-361. (2013)
[Artikel, refereegranskad vetenskaplig]

The degeneration of the Quillen metric for a one-parameter family of Riemann surfaces has been studied by Bismut-Bost and Yoshikawa. In this article, we propose a more geometric point of view using Deligne's Riemann-Roch theorem. We obtain an interpretation of the singular part of the metric as a discriminant and the continuous part as a degeneration of the metric on Deligne products, which gives an asymptotic development involving the monodromy eigenvalues. This generalizes the results of Bismut-Bost and is a version of Yoshikawa's results on the degeneration of the Quillen metric for general degenerations with isolated singularities in the central fiber.

Nyckelord: dual varieties, singularities, discriminant, bundles, curves, space



Denna post skapades 2013-02-15. Senast ändrad 2016-12-20.
CPL Pubid: 173681

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur