A geometric version of the circle method
Tim Browning, W. Sawin
TL;DR
This paper introduces a geometric adaptation of the circle method to compute the cohomology of rational curves on certain affine hypersurfaces, providing new tools for algebraic geometry.
Contribution
It presents a novel geometric circle method and applies it to determine the cohomology of rational curves on low-degree affine hypersurfaces.
Findings
Computed cohomology of rational curves on specific hypersurfaces
Developed a new geometric approach to the circle method
Extended understanding of rational curves in algebraic geometry
Abstract
We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.
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