Normal bundles to Laufer rational curves in local Calabi-Yau threefolds
arXiv:math-ph/0511053 · doi:10.1007/s11005-006-0057-7
Abstract
We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.