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Bibliographic Details
Main Author: Tazoe, Itsuki
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2505.01773
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author Tazoe, Itsuki
author_facet Tazoe, Itsuki
contents We study an asymptotic behavior of the second Chern forms of canonical metrics on a degenerating family of Kähler surfaces with the central fibre having ADE-singularities. We investigate a function on the unit disc defined by fiber integrals of the forms with a smooth test function on the family. We show a lower bound of the Hölder exponent of the function at the origin. Our main results consists of two cases: one is a bound of Hölder exponent along a line for cscK-metrics, using Biquard-Rollin's a priori estimates for cscK-metrics, and the other is a bound of Hölder exponent at the origin for Ricci-flat metrics.
format Preprint
id arxiv_https___arxiv_org_abs_2505_01773
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On asymptotic behavior of the second Chern forms on degenerating Kähler-Einstein surfaces
Tazoe, Itsuki
Differential Geometry
We study an asymptotic behavior of the second Chern forms of canonical metrics on a degenerating family of Kähler surfaces with the central fibre having ADE-singularities. We investigate a function on the unit disc defined by fiber integrals of the forms with a smooth test function on the family. We show a lower bound of the Hölder exponent of the function at the origin. Our main results consists of two cases: one is a bound of Hölder exponent along a line for cscK-metrics, using Biquard-Rollin's a priori estimates for cscK-metrics, and the other is a bound of Hölder exponent at the origin for Ricci-flat metrics.
title On asymptotic behavior of the second Chern forms on degenerating Kähler-Einstein surfaces
topic Differential Geometry
url https://arxiv.org/abs/2505.01773