On infinitesimal deformations and obstructions for rational surface singularities

TL;DR

This paper establishes dimension formulas for the modules T^1 and T^2 associated with rational surface singularities, clarifying their roles in deformation theory and obstruction analysis.

Contribution

It provides new dimension formulas for T^1 and T^2 modules, enhancing understanding of deformation and obstruction spaces for rational surface singularities.

Findings

Dimension formulas for T^1 and T^2 modules derived

T^1 corresponds to the Zariski tangent space of versal deformations

T^2 contains the entire obstruction space in known cases

Abstract

The purpose of this paper is to prove dimension formulas for $T^1$ and $T^2$ for rational surface singularities. These modules play an important role in the deformation theory of isolated singularities in analytic and algebraic geometry. The first may be identified as the Zariski tangent space of the versal deformation of the singularity; i.e. it is the space of infinitesimal deformations. The second contains the obstruction space -- in all known cases it is the whole obstruction space for rational surface singularities.