Infinitesimal deformations of complements of plumbings of rational curves

TL;DR

This paper constructs specific infinitesimal deformations of open domains in smooth projective surfaces, demonstrating that these deformations can alter the complex structure away from the boundary, revealing new insights into surface deformation theory.

Contribution

It introduces a method to construct infinitesimal deformations on complements of plumbings of rational curves, showing they are not trivial and affect the complex structure.

Findings

Infinitesimal deformations can change complex structures away from boundaries.

Constructed deformations are not small, indicating non-trivial deformation behavior.

Provides new examples of deformation phenomena in algebraic geometry.

Abstract

We construct infinitesimal deformations on an open domain of a smooth projective surface given by a complement of plumbings of disjoint linear chains of smooth rational curves. We show that the infinitesimal deformations are not small deformations, that is, they change the complex structure away from the boundary of the domain.