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Towards linear growth for biprojective hypersurfaces of small dimension
Abstract
After removing suitable thin subsets, we count rational points of bounded height on some hypersurfaces of small bidegree in ℙ3×ℙ3 and in ℙ3×ℙ2. One of the ingredients is a new estimate for the number of rational points of bounded height on diagonal quadratic surfaces which improves as the coefficients grow.
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BibTeX
@misc{browning2026towards,
title = {{Towards linear growth for biprojective hypersurfaces of small dimension}},
author = {Tim Browning and Matteo Verzobio},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13163},
eprint = {2610.13163},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13163},
}
RIS
TY - UNPB
TI - Towards linear growth for biprojective hypersurfaces of small dimension
AU - Tim Browning
AU - Matteo Verzobio
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13163
UR - https://arxiv.org/abs/2610.13163
AB - After removing suitable thin subsets, we count rational points of bounded height on some hypersurfaces of small bidegree in ℙ^3×ℙ^3 and in ℙ^3×ℙ^2. One of the ingredients is a new estimate for the number of rational points of bounded height on diagonal quadratic surfaces which improves as the coefficients grow.
ER -