Infinitesimal deformations of complex surfaces with boundary (Q1923270)

We construct infinitesimal deformations of a complex surface \(Y\) with boundary, which is the complement of a tabular neighborhood of a particular negative curve \(C\) in an algebraic surface of general type \(X\). Our infinitesimal deformation is obtained by the restriction of a meromorphic 1-form on \(X\) with a pole at \(C\) to \(Y\). These infinitesimal deformations constitute an infinite dimensional subspace of the infinitesimal deformation space of \(Y\) which has a natural filtration by the order of a pole. Examples are provided by complex hyperbolic surfaces.