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The volume of foliated surfaces with geometric genus one
Abstract
We prove the sharp volume bound vol(ℱ)≥ 1/6 for complex foliated surfaces of general type with positive geometric genus. We also study the equality case and apply the bound to the algebraic integrability and finiteness of small volumes on irregular surfaces.
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BibTeX
@misc{guo2026volume,
title = {{The volume of foliated surfaces with geometric genus one}},
author = {Zhiming Guo and Bokai Hu and Xin Lü},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19788},
eprint = {2610.19788},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19788},
}
RIS
TY - UNPB
TI - The volume of foliated surfaces with geometric genus one
AU - Zhiming Guo
AU - Bokai Hu
AU - Xin Lü
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19788
UR - https://arxiv.org/abs/2610.19788
AB - We prove the sharp volume bound vol(ℱ)≥ 1/6 for complex foliated surfaces of general type with positive geometric genus. We also study the equality case and apply the bound to the algebraic integrability and finiteness of small volumes on irregular surfaces.
ER -