Chern-Ricci flow on Kato surfaces
Abstract
Let S be a Kato surface and D its maximal reduced divisor of rational curves. On S∖ D we construct Hermitian metrics which are flat along the leaves of the canonical foliation and study their evolution under the Chern-Ricci flow. For Enoki surfaces, we construct an immortal normalised solution which, on every compact sublevel of the natural exhaustion, converges in the Gromov-Hausdorff sense to the elliptic base endowed with an explicit flat metric. For Kato surfaces of intermediate type, the affine Green model and its finite-index extension give, under the assumption 0<μ<2, an explicit normalised solution which, on every compact Green block, collapses in the Gromov-Hausdorff sense to a circle. In the Enoki case the limiting area is 2πb2(S); in the intermediate case the length of the limiting circle is determined by the Green and leafwise monodromies.
Related
- Strong Uniqueness for Instantaneously Complete Chern-Ricci Flow
- Finite Time Singularities of Collapsing Kähler Ricci Flow on Ruled Surfaces
- Collapsed Finite Time Singularities of the Kähler-Ricci Flow on Complex Surfaces are of Type I
- Finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I
- Finite Time Singularities of the Kähler Ricci Flow on Compact Kähler Surfaces are of Type I
BibTeX
@misc{angella2026chernricci,
title = {{Chern-Ricci flow on Kato surfaces}},
author = {Daniele Angella and Mauricio Corrêa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18579},
eprint = {2609.18579},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18579},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Chern-Ricci flow on Kato surfaces
AU - Daniele Angella
AU - Mauricio Corrêa
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18579
UR - https://arxiv.org/abs/2609.18579
AB - Let S be a Kato surface and D its maximal reduced divisor of rational curves. On S∖ D we construct Hermitian metrics which are flat along the leaves of the canonical foliation and study their evolution under the Chern-Ricci flow. For Enoki surfaces, we construct an immortal normalised solution which, on every compact sublevel of the natural exhaustion, converges in the Gromov-Hausdorff sense to the elliptic base endowed with an explicit flat metric. For Kato surfaces of intermediate type, the affine Green model and its finite-index extension give, under the assumption 0<μ<2, an explicit normalised solution which, on every compact Green block, collapses in the Gromov-Hausdorff sense to a circle. In the Enoki case the limiting area is 2πb_2(S); in the intermediate case the length of the limiting circle is determined by the Green and leafwise monodromies.
ER -