arXiv subjects

Ruoyi Guo

Publications and source records attributed to Ruoyi Guo.

3 recordsLinked to original sources

arXiv2026

Equidistribution of small points over finitely generated fields

We study the equidistribution of small points over finitely generated fields, in connection with a conjecture of Yuan--Zhang. We first give a counterexample showing that numerical smallness, defined using Moriwaki heights for all polarizations, does not imply equidistribution at every valuation. We then prove that numerically small points do equidistribute at every fully transcendental valuation. In particular, when $F$ is the function field of a curve $B/\mathbb{Q}$, these valuations correspond to points of types $2$, $3$, and $4$ in the Berkovich analytification of $B_{\mathbb{Q}_p}$.

math.NT↗

arXiv2025

Nef cone and successive minima: an example

In this paper, we compute the nef cone and the pseudo-effective cone of $C\times J$ for a smooth projective curve $C$ and its Jacobian variety $J$ such that $C\times J$ has the minimal Picard number. As a consequence, we also compute the successive minima of a height function for the relative setting $C\times J\to J$, and our result shows that Zhang's theorem of successive minima does not hold in this case.

math.AG↗

arXiv2024

An integration formula of Chern forms on quasi-projective varieties

In this paper, I generalize the formula that the integration of Chern forms of hermitian line bundles equals the algebraic intersection number of the underlying line bundles. I generalize it to a formula on a quasi-projective variety over a complete valuation field which might be archimedean or non-archimedean. Our result has a close relation with the integration of Betti forms and the notion of non-degeneracy of a closed subvariety.

math.NT↗