TL;DR
This paper extends the correspondence between line configurations and tautological bundles on rational surfaces to families, using a generalized Fourier-Mukai transform to relate spectral data to bundles over surface fibrations.
Contribution
It introduces a generalized Fourier-Mukai transform that connects spectral data with bundles over rational surface fibrations, expanding existing geometric correspondences.
Findings
Established a new correspondence for families of configurations.
Developed a generalized Fourier-Mukai transform for surface fibrations.
Linked spectral data to bundle structures on rational surfaces.
Abstract
There is a beautiful correspondence between configurations of lines on a rational surface and tautological bundles over that surface. We extend this correspondence to families, by means of a generalized Fourier-Mukai transform that relates spectral data to bundles over a rational surface fibration.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Polynomial and algebraic computation