article published yes Timothy D Browning author 35827D50-F248-11E8-B48F-1D18A9856A870000-0002-8314-0177 Julian Lyczak author Arne Smeets author TiBr department New frontiers of the Manin conjecture project Given a family of varieties over the projective line, we study the density of fibres that are everywhere locally soluble in the case that components of higher multiplicity are allowed. We use log geometry to formulate a new sparsity criterion for the existence of everywhere locally soluble fibres and formulate new conjectures that generalise previous work of Loughran and Smeets. These conjectures involve geometric invariants of the associated multiplicity orbifolds on the base of the fibration in the spirit of Campana. We give evidence for the conjectures by providing an assortment of bounds using Chebotarev’s theorem and sieve methods, with most of the evidence involving upper bounds. https://research-explorer.ista.ac.at/download/21244/21300/2025_AlgebraNumberTheory_Browning.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Mathematical Sciences Publishers2025 eng 1937-0652 1944-7833 2310.0113510.2140/ant.2025.19.2049 19102049-2090 Browning, Timothy D, Julian Lyczak, and Arne Smeets. “Paucity of Rational Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2025. <a href="https://doi.org/10.2140/ant.2025.19.2049">https://doi.org/10.2140/ant.2025.19.2049</a>. Browning TD, Lyczak J, Smeets A. 2025. Paucity of rational points on fibrations with multiple fibres. Algebra &#38; Number Theory. 19(10), 2049–2090. Browning, Timothy D., et al. “Paucity of Rational Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10, Mathematical Sciences Publishers, 2025, pp. 2049–90, doi:<a href="https://doi.org/10.2140/ant.2025.19.2049">10.2140/ant.2025.19.2049</a>. Browning, T. D., Lyczak, J., &#38; Smeets, A. (2025). Paucity of rational points on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/ant.2025.19.2049">https://doi.org/10.2140/ant.2025.19.2049</a> T.D. Browning, J. Lyczak, A. Smeets, Algebra &#38; Number Theory 19 (2025) 2049–2090. Browning TD, Lyczak J, Smeets A. Paucity of rational points on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. 2025;19(10):2049-2090. doi:<a href="https://doi.org/10.2140/ant.2025.19.2049">10.2140/ant.2025.19.2049</a> T. D. Browning, J. Lyczak, and A. Smeets, “Paucity of rational points on fibrations with multiple fibres,” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10. Mathematical Sciences Publishers, pp. 2049–2090, 2025. 212442026-02-16T15:22:19Z2026-07-16T08:52:36Z