Refine search
Actions for selected content:
1 results
Improvements on dimension growth results and effective Hilbert’s irreducibility theorem
- Part of
-
- Journal:
- Forum of Mathematics, Sigma / Volume 13 / 2025
- Published online by Cambridge University Press:
- 19 September 2025, e153
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
We sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree d, over any global field. In particular, we focus on the affine hypersurface situation by relaxing the condition on the top degree homogeneous part of the polynomial describing the affine hypersurface, while sharpening the dependence on the degree in the bounds compared to previous results. We formulate a conjecture about plane curves which provides a conjectural approach to the uniform degree
$3$ case (the only remaining open case). For induction on dimension, we develop a higher-dimensional effective version of Hilbert’s irreducibility theorem, which is of independent interest.
