The main aim is to create a comprehensive atlas for all-length wall fibers and analyze their geometrical properties.
Construction of a global projective atlas for wall fibers.
Identification of the Segre wall and canonical blow-up in the context of algebraic geometry.
Analysis of the Atiyah flop and its associated small resolutions.
Successfully identified the Segre wall and canonical blow-up as crucial elements in the atlas.
Established relationships between different small resolutions via the Atiyah flop.
Abstract
We construct a global projective atlas for all-length wall fibers, identifying the Segre wall, canonical blow-up, and the two small resolutions related by the Atiyah flop.