Deformations of the logarithmic tangent bundle of smooth projective surfaces
Sukmoon Huh, Min-Gyo Jeong
Source 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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