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PreprintCC BY 4.0arXiv

Deformations of the logarithmic tangent bundle of smooth projective surfaces

  • Sukmoon Huh
  • Min-Gyo Jeong
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Abstract

We study fixed-determinant deformations of the logarithmic tangent bundle associated with a smooth irreducible divisor on a smooth complex projective surface. We derive numerical criteria for the existence of positive-dimensional deformation families. Using the Enriques--Kodaira classification and Miyaoka-type inequalities, we classify the minimal surface pairs whose logarithmic tangent bundle is infinitesimally rigid. We also prove monotonicity under compatible blow-ups and compute local comparison formulas for resolutions of low-multiplicity ordinary singularities of the boundary.

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Cite

BibTeXRIS
BibTeX
@misc{huh2026deformations,
  title = {{Deformations of the logarithmic tangent bundle of smooth projective surfaces}},
  author = {Sukmoon Huh and Min-Gyo Jeong},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35127},
  eprint = {2610.35127},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35127},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Deformations of the logarithmic tangent bundle of smooth projective surfaces
AU  - Sukmoon Huh
AU  - Min-Gyo Jeong
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35127
UR  - https://arxiv.org/abs/2610.35127
AB  - We study fixed-determinant deformations of the logarithmic tangent bundle associated with a smooth irreducible divisor on a smooth complex projective surface. We derive numerical criteria for the existence of positive-dimensional deformation families. Using the Enriques--Kodaira classification and Miyaoka-type inequalities, we classify the minimal surface pairs whose logarithmic tangent bundle is infinitesimally rigid. We also prove monotonicity under compatible blow-ups and compute local comparison formulas for resolutions of low-multiplicity ordinary singularities of the boundary.
ER  -