On deformations of unions of planes in projective space (Q1358204)

Suppose \(T\) is a triangulation of a connected compact manifold of dimension 2 possibly with boundary and let \(X\) be the surface of \(T\) in projective space \(\mathbb{P}^g\). The cohomology of the normal sheaf \({\mathcal N}_X\) of \(X\) in \(\mathbb{P}^g\) and the sheaf of obstructions \({\mathcal T}_X^2\) of \(X\) are computed. By computing local extensions of the first-order embedded deformations of \(X\) in \(\mathbb{P}^g\), we find necessary and sufficient conditions on \(T\) so that \(X\) is unobstructed.